- 9 times the side of one square exceeds (#3248)
9 times the side of one square exceeds the perimeter of the second square by 1 metre and 6 times the area of the second square exceeds 29 times the area of the first by 1 square ...
solving systems of equations, systems of equations, solving equations, systems, equations
- A 240 inches pipe is cut into two pieces (#60)
A 240 inches pipe is cut into two pieces. One piece is 3 times the length of the ...
solving equations, equations
- A 240-inch pipe is cut into 2 pieces (#1495)
A 240-inch pipe is cut into 2 pieces. One piece is 3 times the length of the ...
solving equations, equations
- A 63 inch pipe is cut into two pieces (#2947)
A 63 inch pipe is cut into two pieces. If one piece has a length of z inches, what is the length, in ...
equations
- A ball costs $1.25 and a bat costs $79.00 (#1576)
A ball costs $1.25 and a bat costs $79.00. The team only has 150...
equations, algebraic equations
- A ball is shot into the air (#3415)
A ball is shot into the air. It's height , h in metres after t seconds is modeled by h=-4.9t2 + 30t +1.6...
solving equations, quadratic equations, solving quadratic equations, equations
- A balloon is rising from the ground (#457)
A balloon is rising from the ground at 4 feet per second. Another balloon is at 756 feet and descending at 3 feet per ...
substitution method, solving quadratic equations, quadratic equations, solving equations, equations, equations
- A balloon is rising from the ground (#457)
A balloon is rising from the ground at 4 feet per second. Another balloon is at 756 feet and descending at 3 feet per ...
substitution method, solving quadratic equations, quadratic equations, solving equations, equations, equations
- A bike shop rents mountain bikes (#3256)
A bike shop rents mountain bikes for a $8.50 insurance charge plus $3.50 per hour. For how many hours can a person rent a bike with $32...
systems of linear equations, systems of equations, linear equations, systems, equations
- A boat traveled 126 miles (#86)
A boat traveled 126 miles downstream and back. The trip downstream took 6 hours. The trip back took 42 ...
systems of equations, systems, equations
- A boy is now two-thirds as old (#1293)
A boy is now two-thirds as old as his sister, and two years ago he was five-eighths as old as she was ...
algebraic equations, equations
- A boy walked at the rate (#1775)
A boy walked at the rate of 2mph and then rode a bicycle back the same distance at the rate of 10mph. If the entire trip took 3 ...
systems of equations, systems, equations
- A bulldozer can move 25 tons/h of material (#2440)
A bulldozer can move 25 tons/h of material,and an end loader can move 18 tons/h.The bulldozer costs $75/h to operate,and the end loader costs $%0/h to operate.During a 1 hour construction company moved 204 tons at a cost of $600...
systems of linear equations, systems of equations, linear equations, systems, equations
- A candy shop sells two new flavors of candy (#2471)
A candy shop sells two new flavors of candy. Chewy nut and chocolate chew. Each barrel of chewy nut requires 8 pounds of nuts and 4 pounds chocolate and has a profit of $540. Each barrel of chocolate chew requires 8 pounds of nuts and 2 pounds of chocolate and has a profit of $210. There are 64 pounds of nuts and 32 pounds of chocolate in stock, and the owner does not want to buy more stock to make the ...
systems of equations, systems, equations
- A car leaves New York traveling south (#3115)
A car leaves New York traveling south at 50 m/hr. One hour later, another car leaves New York on the same road traveling south at 55m/...
systems of equations, systems, equations
- A chemical plant is rectangular and has a length (#1721)
A chemical plant is rectangular and has a length of a hundred meters and a width of sixty meters. A safety zone of uniform width surrounds the plant. if the area of the safety zone equals the area of the ...
solving systems of equations, systems of equations, solving equations, systems, equations
- A child in an airport is able to cover (#2781)
A child in an airport is able to cover 291 meters in 3 minutes running at a steady speed down a moving sidewalk in the direction of the sidewalk's motion. Running at the same speed in the direction opposite to the sidewalk's movement, the child is able to cover 228 meters in 4 minutes. What is the child's running speed on a still ...
equations, speed
- A circle with radius 5 (#261)
A circle with radius 5 has its center at (4,1). the line x-2y+4=0 intersects the circle. find the intersections
circle equation, circles, equations, plane figures, shapes, curves
- A community center sells (#1806)
A community center sells a total of $301 tickets for a basketball game. An adult ticket costs $3. A student ticket costs $1. The sponsors collect $487 in ticket ...
systems of equations, systems, equations
- A company borrowed 600,000 for one year (#2375)
A company borrowed 600,000 for one year. Part was at 8% interest, part was at 10% interest rate. How much at each rate if annual interest is $53...
systems of equations, solving systems of equations, systems, equations, solving equations
- A construction worker is working on the roof (#3013)
A construction worker is working on the roof of a building. A drop of paint falls from a rafter that is 225 feet above the ...
polynomial equations, equations
- A cricket jumps off the ground (#3012)
A cricket jumps off the ground with an initial vertical velocity 4 feet per second.
a. Write an equation that gives the height (in feet) of the cricket as a function of the time (in seconds) since it jumps.
...
polynomial equations, equations
- A farmer raises wheat and soybeans (#2536)
A farmer raises wheat and soybeans on 215 acres. if he wants to plant 31 more acres in wheat than ...
systems of equations, systems, equations
- A framer at a photo gallery (#516)
A framer at a photo gallery wants to frame a print with a matte of uniform width all around the print. To make it pleasing to the eye, the area of the matte should equal the area of the print. If the print measures 40 cm by 60 ...
solving equations, solving quadratic equations, quadratic equations, equations
- A grocer plans to mix candy (#809)
A grocer plans to mix candy that sells for $2 a pound with candy that sells for $4 a pound to get a mixture that sells for $2.75 a ...
systems of equations, systems, equations
- A machine produces open boxes (#3217)
A machine produces open boxes using square sheets of plastic. The machine cuts equal sized squares measuring 2 inches on a side from each corner of the sheet, and then shapes the plastic into an open box by turning up th esides. If each box must have a volume of 242 cubic inches, find the length of one side of the open ...
quadratic equations, equations
- A man buys x cans of beer (#1238)
A man buys x cans of beer at 30 cents each and (x+4) cans of lager at 35 cents each. The total cost is $3.35...
solving equations, equations
- A mixture of 12 liters of chemical A (#2030)
A mixture of 12 liters of chemical A, 16 liters of chemical B, and 26 liters of chemical C
is required to kill a certain destructive crop insect. Commercial spray X contains 1, 2, and 2
parts, respectively, of these chemicals. Commercial spray Y contains only chemical C.
Commercial spray Z contains only chemicals A and B in equal ...
equations, systems of equations, systems
- A model rocket is shot into the air (#3116)
A model rocket is shot into the air and its path is approximated by h = -5t2 + 30t where h is the height of the rocket above the ground in metres and t is the elapsed time in ...
solving quadratic equations, quadratic equations, solving equations, equations
- A motor boat travels (#2261)
A motor boat travels 400km. If the boat went 18km/h faster, it could have traveled 600 km in the same amount of ...
completing the square, solving quadratic equations, quadratic equations, solving equations, equations
- A motorboat travels 332 in 4 hours (#2571)
A motorboat travels 332 in 4 hours going upstream 555 and in 5 hours going downstream. What is the speed of the boat in still ...
systems of linear equations, systems of equations, linear equations, systems, equations
- A motorcycle breaks down and the rider (#1171)
A motorcycle breaks down and the rider has to walk the rest of the way to work. The motorcycle was traveling at 45 mi/hr, and the rider walks at a speed of 6 mi/hr. The distance from home to work is 25 miles, and the total time of the trip was 2 ...
equations, systems, systems of equations
- A parallelogram has a base (#2178)
A parallelogram has a base of length 2x +1 and a height of x+3 and has an area of 42 square units. Find the base and height of the parallelogram. (A=BH)
solving quadratic equations, quadratic equations, solving equations, equations
- A park is twice as long as it is wide (#2832)
A park is twice as long as it is wide. It's length is 30...
area, shapes, plane figures, solving equations, equations
- A pet store has a total of 35 dogs (#2526)
A pet store has a total of 35 dogs, cats, and ...
multi step equations, equations
- A piggy bank contains 20 coins (#378)
A piggy bank contains 20 coins, consisting of nickels and dimes. How many of each type of coin are there if the piggy bank contains $1...
solving equations, equations
- A pilot flies 630 miles with a tail wind (#2646)
A pilot flies 630 miles with a tail wind of 35 miles per hour. Against the wind, he flies only 455 miles in the same amount of ...
solving rational equations, solving equations, rational equations, equations
- A rectangle corral is to be built (#2014)
A rectangle corral is to be built using 70m of fencing. If the fencing has to enclose all four sides of the ...
solving equations, quadratic equations, equations, solving quadratic equations, completing the square
- A rectangle`s width is 4 times the length (#3542)
A rectangle's width is 4 times the length. The perimeter is 30 ...
solving systems of equations, systems of equations, solving equations, systems, equations
- A rectangular garden is 5 feet longer (#3477)
A rectangular garden is 5 feet longer than twice its width. It has a sidewalk 3 feet wide on two of its sides. The area of the sidewalk is 213 square ...
systems, solving systems of equations, systems of equations, polynomials, solving equations, equations
- A rectangular lot whose perimeter (#2249)
A rectangular lot whose perimeter is 360 ft. is fenced along 3 sides. An expensive fencing along the lot's length costs $20 per ft. and an inexpensive fencing along the 2 side widths costs $8 per ft. The total cost of the fencing along the 3 sides comes to $3280...
systems of linear equations, systems of equations, linear equations, systems, equations
- A rectangular patio is 7 ft longer (#1448)
A rectangular patio is 7 ft longer than it is ...
solving systems of equations, systems of equations, solving equations, systems, equations
- A running track has straight sides and a semicircular ends (#3339)
A running track has straight sides and a semicircular ends. If the length of the track is 440 yd and the two straight parts are each 110 yd ...
curves, shapes, plane figures, circle equation, circles, equations
- A software development company is getting ready (#3053)
A software development company is getting ready to release a new product. The QA Director is notified the following: A Junior Verification Engineer takes 1 hour longer to fix a bug than it takes a Senior Engineer. If they can fix the bug in 5 hours working ...
solving rational equations, solving equations, rational equations, equations, work rate, rate
- A supplier gives a quote for you (#57)
A supplier gives a quote for you: $3000 for 500 t-shirts; $5500 for 1000
t-shirts.
Assume there is a linear relationship between the number of t-shirts ordered (n) and the total cost (C)...
solving equations, equations
- A total of $8000 is invested in two funds (#1134)
A total of $8000 is invested in two funds paying 4% and 5% annual interest. The combined annual interest is $350...
systems of equations, systems, equations
- A total of 50 juniors and seniors (#3206)
A total of 50 juniors and seniors were to give a mathmatics test. The 35 juniors attained an average score of 80 while the 15 sneiors attained an average of 70...
polynomial equations, equations
- A total of 512 tickets were sold (#3120)
A total of 512 tickets were sold for the school play. The number of student tickets sold was three times the number of adult tickets ...
systems of equations, systems, equations
- A town`s old street sweeper (#990)
A town's old street sweeper can clean the streets in 60 h. The old sweeper together with a new sweeper can clean the streets in 15 ...
fractional equations, equations, work rate, rate
- AB is one of the direct common tangent (#1085)
AB is one of the direct common tangent of two circles with radius 12 cm and 4 cm respectively touching each ...
circle equation, circles, equations, plane figures, shapes, curves
- Ahmed has first half of a treasure map (#1104)
Ahmed has first half of a treasure map, which indicates that the treasure is buried in the desert (2x + 6) paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must go to the Castle Rock, walk ‘x’ paces to the North, and then walk (2x + 4) paces to the East. If they share their information, then they can find ‘x’ and save a lot of ...
completing the square, solving quadratic equations, quadratic equations, solving equations, equations
- Ahmed has half of a treasure map (#3297)
Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find
the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they can find x and save a lot of ...
equations
- Alvin is 15 years older than Elga (#3370)
Alvin is 15 years older than Elga. The sum of their ages is 85...
equations, solving systems of equations, systems of equations, solving equations, systems
- Amy took a test that had a math section (#2229)
Amy took a test that had a math section and an English section. She earned a total score of 88. Her math score was 6 points higher than her English ...
systems of equations, systems, equations
- An intake pipe can fill a certain tank (#448)
An intake pipe can fill a certain tank in 6 hours when the outlet pipe is closed, but with the outlet pipe open it takes 9 ...
fractional equations, equations
- Andres and Biloy working together (#921)
Andres and Biloy, working together, can build a chicken house in 6 2/3 hours. Andres became ill after 3 hours of working with Biloy, and Biloy finished the job, continuing to work alone in 8 1/4 more ...
solving systems of equations, systems of equations, solving equations, systems, equations, work rate, rate
- April buys eight books (#197)
April buys eight books for $44. Paperback books cost $4 and hardback cost $8...
systems, equations, systems of equations
- Aprroximately 4.5 million wrecked cars (#233)
Aprroximately 4.5 million wrecked cars are recycled in two consecutive years. There were 700,000 more recycled the second year than the first ...
solving equations, equations, systems of equations, systems, solving systems of equations
- At a point 30 meters from the base of the tower (#3524)
At a point 30 meters from the base of the tower, the distance to the top of the tower is 2 meters more than twice the height of the ...
equations, quadratic equations
- At an IMAX theatre, the giant rectangular screen (#3321)
At an IMAX theatre, the giant rectangular screen has a width 36 feet less than its length. If the perimeter of the screen is 332 ...
systems of equations, systems, equations
- At full speed, an airplane can travel (#1815)
At full speed, an airplane can travel 4500 miles with the wind in 6 hours, but it requires 10 hours to travel the same distance against the wind.
what is the wind ...
systems of equations, systems, equations
- At the afternoon matinee movie (#1982)
At the afternoon matinee movie 3 adult tickets and 4 child tickets cost $41, and 4 adult tickets and 3 child tickets cost $43...
linear equations, equations, systems of equations, systems, systems of linear equations
- At the animal shelter (#467)
At the animal shelter there were 46 cats and dogs. There were 18 more dogs than ...
solving equations, equations
- Bob, driving a new Ford (#200)
Bob, driving a new Ford, travels 330 miles in the same amount of time it takes John, driving and old Chevy and traveling 10 miles per hour faster, to travel 390 ...
solving rational equations, solving equations, equations, rational equations
- Bob, traveling in a new Ford (#2512)
Bob, traveling in a new Ford, travels 330 miles in the same amount of time it takes John, driving an old Chevy 10 miles per hour faster, to travel 390. How fast is Bob ...
equations
- Car 1 leaves St. Louis at 12 noon (#1358)
Car 1 leaves St. Louis at 12 noon, traveling at 52mph. Car 2 leaves St. Louis at 2 pm, but travels at 72mph, going in the same ...
solving equations, equations
- Cary spent 1/3 of his time working on fractions (#1595)
Cary spent 1/3 of his time working on fractions and 3/6 of his time working on algebra. He spent the last 10 minutes of his class reading a chapter in his ...
equations, fractional equations
- completing the square (#505)
The path of the ball for many golf shots can be modeled by a quadratic function. The path of a golf ball hit at an angle of about 10 degrees to the horizontal can be modeled by the function, h= -0.002d2 + 0.4d, where h is the height of the ball, in meters, and d is the horizontal distance the ball travels, in meters, until it first hits the ground.
a) What is the maximum height reached by the ball?
b) What is the horizontal distance of the ball from the golfer when the ball reaches its maximum ...
completing the square, solving quadratic equations, quadratic equations, solving equations, equations
- completing the square (#737)
change to vertex-axis form by completing the square
f(x)=x2+4x-5
completing the square, solving quadratic equations, quadratic equations, solving equations, equations
- copper that was 63% pure (#1100)
copper that was 63% pure was melted together with copper that was 90% pure to make 18 kilograms of an alloy that was 75% ...
equations, systems, systems of equations
- Crane A can unload the container ship (#2040)
Crane A can unload the container ship in 10 hours, and crane B can unload it in 14 hours. Crane A started to unload the ship at noon and was joined by crane B at 2 P....
fractional coefficients, coefficients, equations, algebraic equations, algebraic expressions, algebraic fractions, expressions
- Danny had $22.00 in loonies and toonies (#48)
Danny had $22.00 in loonies and toonies.
a) Write a linear relation for the total amount of money in terms of the number of loonies and toonies.
b) Write an equation to express the number of toonies in terms of the number of ...
solving equations, equations
- Dave sold popcorn and pretzels (#1057)
Dave sold popcorn and pretzels at the game. He sold a told of $336 worth of both. He sold popcorn for $2.50 and pretzels for $2 each. He sold twice as many bags of popcorn than ...
systems, systems of equations, equations
- Diophantus was a famous Greek mathematician (#1045)
Diophantus was a famous Greek mathematician who lived and worked in Alexandria, Egypt, probably in the third century A.D. After he died, someone described his life in this puzzle:
He was a boy for 1/6 of his life.
After 1/12 more, he acquired a beard.
After another 1/7, he married.
In the fifth year after his marriage his son was born.
The son lived half as many years as his father.
Diophantus died 4 years after his ...
fractional equations, equations
- division equations (#77)
I have 9 boxes and each box contains equal number of ...
division equations, equations
- During a used book sale (#871)
During a used book sale, a total of 62 books were sold and $103 was made. The books were priced at $1.50 or $2.00 each. Find how many books are sold at $1.50 and how many at $2.00
systems of equations, systems, equations
- Erica hiked up a mountain trial (#1003)
Erica hiked up a mountain trial at 3km/h and returned at 4k/h. The entire trip took five hours 10 min including the half an hour she spent at the ...
equations, fractional coefficients, expressions, coefficients, algebraic fractions, algebraic expressions, algebraic equations
- Find a two-digit number (#1353)
Find a two-digit number where the sum of the digits is 6 and the number is 6 times the unit's digit.
systems of equations, systems, equations
- Find an equation of variation y (#1257)
Find an equation of variation y varies jointly as w and the square of x and inversely as z, y=25 when x=5 w=5 and z=10
solving equations, equations
- Find the area of a circular flower bed (#471)
Find the area of a circular flower bed with a diameter of 54 feet.
equations, solving equations
- Find the value of two numbers (#2965)
Find the value of two numbers if their sum is 12 and their difference is 4
systems of equations, systems, equations
- Flex drove 800 miles in x hours (#832)
Flex drove 800 miles in x hours on Monday
a) write a rational expression for his average speed.
b) On tuesday he drove for 6 hours at the same average ...
solving rational equations, solving equations, equations, rational equations
- Four times a number (#1320)
Four times a number is 21 more than the number.
solving equations, equations
- Frank`s Specialty Coffees makes (#1030)
Frank's Specialty Coffees makes a house blend from two types of coffee beans, one selling for $9.05 per pound, and the other selling for $6.25 per pound. His house blend sells for $7.37 per pound. If he is using 9lb of the 6.25/lb beans, how many pounds of the $9...
substitution method, solving quadratic equations, quadratic equations, solving equations, equations
- George`s mom spent 3 times as much money (#1510)
George's mom spent 3 times as much money on fruit than dairy products. She spent twice as much on dairy products than cereal. If her bill was $48.75...
multi step equations, equations
- Harry can paint a room in 3 hours (#3142)
Harry can paint a room in 3 hours, and Kerry can paint it in 4 ...
equations, work rate, rate
- How do the Quarter Pounder and Whopper (#422)
How do the Quarter Pounder and Whopper with cheese measure up in the calorie department? Actually, not too well. Two Quarter Pounders and three whoppers with cheese provide 2607 calories. Even with one of each provides enough calories to bring tears to Jenny Crag's eyes-9 calories in excess of what is allowed on a 1000 calories-a-day ...
substitution method, solving quadratic equations, quadratic equations, solving equations, equations
- I bought a can of varnish (#2542)
I bought a can of varnish and store at temperature of 40 degree. I change to another place where the temperature was 74degree. After 2 hours the temperature of the varnish was 58 degree .If the temperature of varnish must be 68 degree for best results ...
logarithmic equations, equations, logarithms
- I have $50 consisting of all $5 bills and $1 bills (#3184)
I have $50 consisting of all $5 bills and $1 bills and total of 22 ...
systems of equations, systems, equations
- I think of a number (#3296)
I think of a number. I add 100 and subtract 10. My answer is -100...
equations
- If 3 times the second number (#2018)
If 3 times the second number is subtracted from the sum of the first number and 3 times the third ...
systems of equations, systems, equations
- If a certain number is added to both the numerator and denominator (#2663)
If a certain number is added to both the numerator and denominator to the fraction 7/9, the result is 5/7...
rational equations, equations
- If a ladder is leaning against a building (#2714)
If a ladder is leaning against a building, and the distance from the bottom of the ladder to the building is 8 ft. less than the length of the ladder, how high up the side of the building is the top of the ladder if the distance is 1 ...
right triangles, solving algebraic equations, pythagorean theorem, triangles, polygons, shapes, curves, plane figures, algebraic equations, solving equations, equations
- If jennifer were three times as old (#3009)
If Jennifer were three times as old as she was five years ago, she will be twenty seven more than current ...
systems of equations, systems, equations
- If robert has ten coins all nickels and dimes (#1830)
If robert has ten coins all nickels and dimes worth 70 cents how many of each kind of coin does he have?
linear equations, equations
- If the length of each side of a square is decreased (#1609)
If the length of each side of a square is decreased by 4 inches, the perimeter of the new square is 10 inches more than half the perimeter of the original ...
equations, solving equations
- If the price of 3 hats and 7 shirts (#2047)
If the price of 3 hats and 7 shirts is $189 and 5 hats and 11 shirts is $301...
equations, systems, systems of equations
- It costs $5 to become a new member (#802)
It costs $5 to become a new member of a book club. There is a $10 charge per book ordered and tax is 7% on the books. Shipping and handling is free for all members. How many books were purchased by a new member if the total bill comes to $69...
multi step equations, equations
- Jill ran up the hill (#1252)
Jill ran up the hill at 6 km/hr and down at 10 km/...
fractional equations, equations
- Juan goes to a bank and gets change (#1061)
Juan goes to a bank and gets change for a $50 bill consisting of all $5 and $1 bills. There are 22 bills in ...
equations, systems, systems of equations
- Jurassic Park charges $20 for adults (#3468)
Jurassic Park charges $20 for adults and $12 for children. Total bill for 454 people was $3860...
systems, polynomials, solving systems of equations, systems of equations, solving equations, equations
- Kaya pasted 3 rows of photos (#1185)
Kaya pasted 3 rows of photos on each of 5 pages of her scrapebook. She put 2 photos in each ...
multi step equations, equations
- Lara arranged the books on her shelf by size (#2520)
Lara arranged the books on her shelf by size. 2/10 of the books were tall, and 1/2 of the books were ...
linear equations, equations
- Mark bought 114 meters of fencing (#3288)
Mark bought 114 meters of fencing to enclose an area of pasture for his sheep. He plans to use all of the fencing to make a rectangle that is twice as long as it is ...
solving systems of linear equations, systems of linear equations, systems of equations, linear equations, systems, equations
- midpoint (#150)
If ab=6, bc=9 and ac=13, what must be true of points a,...
midpoint formula, equations, line equations
- Mike bought 3 cokes and 2 fries (#2307)
Mike bought 3 cokes and 2 fries and paid 5.25. he also noticed the cost of an order of fries is 2 times the cost of a ...
systems of equations, systems, equations
- multi-step equations (#1019)
Twelve less than the quotient of the number and 7 is -2
multi step equations, equations
- My friends and I went to the mall (#343)
My friends and I went to the mall last Saturday. We went into Hollister. A shirt was on sale for $25.00 . 5 times the cost of the skinny jean minus the cost of the shirt equals $300.00...
multi step equations, equations
- One eighth of a number (#1151)
One eighth of a number is ten less than one fifth of the ...
fractional equations, equations
- One positive integer is 8 less (#816)
One positive integer is 8 less than twice another and the sum of their squares is 244
equations, systems of equations, solving quadratic equations, solving systems of equations, quadratic equations, solving equations, systems
- Paul bought 8 eating utensils (#2057)
Paul bought 8 eating utensils for a total of $26. Spoons cost $4 and forks cost $3...
systems of equations, systems, equations
- radical equations (#130)
The formula for velocity is v = (sqrt. 2gh)...
radical equations, equations, radicals, numbers, number sense
- Ravi will be four times his present age (#2102)
Ravi will be four times his present age after five ...
linear equations, equations
- Ruby is 6 years younger than Carlo (#3274)
Ruby is 6 years younger than Carlo. The average of their ages now, is twice Ruby's age 5 years ...
solving systems of equations, systems of equations, solving equations, systems, equations
- Rudy must play 12 commercials (#2240)
Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 sec or 60 sec long. If the total commercial time during that hour is 10 ...
solving equations, equations
- Rudy must play 12 commercials (#3521)
Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 sec or 60 sec long. If the total commercial time during that hour is 10 ...
equations, solving systems of equations, systems of equations, solving equations, systems
- Sally can paint a house in 4 hours (#1790)
Sally can paint a house in 4 hours. John can paint the same house in 6 ...
solving rational equations, solving equations, rational equations, equations, work rate, rate
- Sam takes 6 days less than the number of days (#2982)
Sam takes 6 days less than the number of days taken by John to complete a piece of work. If both Sam and John together can complete the same work in 4 ...
quadratic equations, equations, work rate, rate
- Sarah had an idea (#234)
Sarah had an idea, what would happen if you put a golf ball inside a basketball? How much room would there be inside the basketball afterwards. Her golf ball has a radius of 1.68 inches while her basketball has a diameter of 9.4 ...
circle equation, circles, equations, plane figures, shapes, curves
- Shelly can paint a fence in 8 hours (#2107)
Shelly can paint a fence in 8 hours. Karen can do it in 4 ...
solving rational equations, solving equations, rational equations, equations
- Shoes cost $20 per pair and boots cost $60 per pair (#1722)
Shoes cost $20 per pair and boots cost $60 per pair. Arlene and Jerry spent $8000 and bought 3 times as many boots as ...
systems of equations, systems, equations
- Simone has 16 player on her soccer team (#121)
Simone has 16 player on her soccer team. There are 6 more boys than ...
systems of equations, solving systems of equations, systems, equations, solving equations
- Six times a number decreased by five (#312)
6 times a number decreased by 5 is the same as 4 times the number increased by 9...
linear equations, equations
- Stella’s Catering is planning a wedding reception (#3186)
Stella’s Catering is planning a wedding reception. The bride and groom would like to serve a nut mixture containing 25% peanuts. Stella has available mixtures that are either 40% or 10% ...
equations
- Suppose that an object is 100 pounds (#163)
Suppose that an object is 100 pounds when it is at sea level. Find the value of C that make the equation true. Sea level is 3...
solving radical equations, solving equations, equations, radical equations
- Suppose you decide to move your garden (#892)
Suppose you decide to move your garden away from the house, so you have to use 50 feet of fencing for four sides. The length of the garden must be twice as long as the width. If the area is now 139 feet ...
equations, solving equations, quadratic equations, completing the square, solving quadratic equations
- Suppose you invest $2000 today (#719)
Suppose you invest $2000 today and you don't add or subtract anything from the money to your investment for 30 yrs. If you earn 12% per year on your investment every year for 30 ...
solving polynomial equations, polynomial equations, solving equations, equations
- systems of equations (#87)
The school that Asanji goes to is selling tickets to a play. On the first day of ticket sales the school sold 10 senior citizen tickets and 9 student tickets for a total of $200. The school took in $87 on the second day by selling 7 senior citizen tickets and 1 student ...
systems of equations, systems, equations
- Systems Of EquationsThe sum of three consecutive numbers (#1640)
The sum of three consecutive numbers is the same as twice the value of the last ...
equations, systems, systems of equations
- Tasty Bakery sells three kinds of muffins (#2235)
Tasty Bakery sells three kinds of muffins: chocolate chip muffins at 25 cents each, oatmeal muffins at 30 cents each, and cranberry muffins at 35 cents each. Charles buys some of each kind and chooses three times as many cranberry muffins as chocolate chip muffins. If he spends $4.70 on 15 ...
systems of equations, systems, equations
- The area of a triangle (#3232)
The area of a triangle is 30in2. The base of the triangle measures 2 in. more than twice the height of the ...
systems of equations, solving systems of equations, triangles, polygons, shapes, plane figures, curves, solving equations, systems, equations
- The band boosters are organizing a trip (#2976)
The band boosters are organizing a trip to a national competion for the 226-member marching band. A bus will hold 70 students and their instruments. A van will hold 8 students and their instuments. A bus costs $280 to rent for the trip. A van costs $70 to rent for the trip. The boosters have $980 to use for ...
solving systems of linear equations, systems of linear equations, systems of equations, linear equations, systems, equations
- The board of directors of a corporation (#3364)
The board of directors of a corporation grant a bonus of $5000 to be divided between two employees. The senior employee receives $1200 more than the junior ...
linear equations, systems of equations, systems of linear equations, solving systems of linear equations, systems, equations
- The chief executive has just requested (#2911)
The chief executive has just requested that Suzie's division make 300 gallons of sparkling water to sell at $6 per gallon. She wishes to mix 3 grades of water selling for $9, $3, $4.50. She must use twice as much of the 4.50 water as the 3.00...
systems of equations, systems, equations
- The difference of a positive number (#3073)
The difference of a positive number and its square is -30...
completing the square, solving quadratic equations, quadratic equations, solving equations, equations
- The difference when 7 less than a number (#2843)
The difference when 7 less than a number is subtracted from twice the number is 12...
equations
- The fencing to surround a flower garden (#3051)
The fencing to surround a flower garden 14 feet by 9 feet costs $8 per ...
equations
- The following table gives the population (#202)
The following table gives the population (in millions) of Georgia and North Carolina in 1990 and 2003.
Year Georgia North Carolina
1990 6.5 6.8
2003 8.7 8.4
Assume that the population growths are ...
linear equations, equations
- The formula represents the number of households (#2278)
The formula N=4x2+5x+1 represents the number of households N, in thousands, in a certain city that have a computer x years after 1990. According to the ...
systems of equations, systems, equations
- The height of a batted baseball as a function of time (#3535)
The height, H metres, of a batted baseball as a function of time, t seconds, since the ball was hit can be modeled by the relation H=-2.1(t-2.4)2+13.
a) what was the maximum height of the ball?
b) at what time after it was first hit did the ball reach its maximum height?
c) how far off the ground was the ball first ...
equations, solving equations, completing the square, quadratic equations, solving quadratic equations
- The hypotenuse of a right triangle (#2792)
The hypotenuse of a right triangle is 16 in. longer than the shortest side and 2 in. longer than the
remaining ...
right triangles, triangles, polygons, shapes, plane figures, curves, solving systems of equations, solving equations, systems of equations, equations, systems
- The length of a certain rectangle (#3290)
The length, L, of a certain rectangle is four feet more than three times its width, W. The perimeter of the rectangle is 88 ...
solving systems of equations, rectangles, perimeter, shapes, plane figures, systems of equations, solving equations, systems, equations
- The length of a rectangle is 2 feet more (#1401)
The length of a rectangle is 2 feet more than twice the width. The perimeter of the rectangle is 40 square feet. Find the length and width of the rectangle. (Hint: First write the length using an algebraic expression that contains width)
solving equations, systems of equations, solving systems of equations, systems, equations
- The length of a rectangle is 4 feet longer (#1400)
The length of a rectangle is 4 feet longer than twice its width. If the area is 96 square ...
solving quadratic equations, quadratic equations, solving equations, equations
- The length of a rectangle is 5 cm less (#3369)
The length of a rectangle is 5 cm less than twice the width. If the area of the rectangle is 88 cm ...
area, equations, plane figures, shapes, solving equations
- The length of a rectangular field (#3277)
The length of a rectangular field is 24 meters. This is 3 meters less than twice the ...
systems of equations, systems, equations
- The numerator of a fraction (#2418)
The numerator of a fraction is 19 less than the denominator. If the value of the fraction is 3/8...
fractional equations, equations
- The owner of a health foods store (#254)
The owner of a health foods store determines that the demand equation for sellin a nutritional supplement is p=18 - 0.5 square root ((x-4) where p is the price of dollars and x is the number of bottles demanded per ...
solving radical equations, solving equations, equations, radical equations
- The perimeter of a court is 108 meters (#3526)
The perimeter of a court is 108 meters. If the length is 6 meters longers than twice the ...
equations, systems of equations, systems, solving equations, solving systems of equations
- The perimeter of a rectangular (#3046)
The perimeter of a rectangular lawn is 24m. If the area of the lawn is 35m2...
perimeter, shapes, solving equations, systems of equations, equations, systems, solving systems of equations
- The perimeter of Mrs. McCord`s rectangular garden (#734)
The perimeter of Mrs. McCord's rectangular garden is 100 feet. If the length is 1.5 times longer than the ...
substitution method, solving quadratic equations, quadratic equations, solving equations, equations
- The population of black mountain (#2557)
The population of black mountain is 40,000 and is gowing by 800 per year. The population of Hidden Valley is 67,000 and is decreasing by 550 per ...
linear equations, equations
- The product of two consecutive positive even intergers (#2818)
The product of two consecutive positive even intergers is one hundred sixty-...
algebraic equations, equations
- The product of whole positive even integer (#322)
The product of whole positive even integer and the product of the next larger positive integer equals the reciprocal of the first ...
linear equations, equations
- The restaurant can currently seat 120 people (#2640)
The restaurant can currently seat 120 people up to 4 people in each booth and up to 8 people in each table. Plan a new seating arrangement with no more than 12 sections that will hold a total of 250 people. Each section should have no more than 6 table or 6 booths and no section may have ...
equations
- The side of a square house is 24 ft long (#1913)
The side of a square house is 24 ft long, and the house is located on a lot which is 50 ft longer than it is wide. The perimeter of the lot is 20 ft more than 5 times the perimeter of the ...
solving systems of equations, systems of equations, solving equations, equations, systems
- The sum of 2 numbers (#2654)
The sum of 2 numbers is 30, and their quotient is 2/3...
fractional equations, equations
- The sum of the digits of a two-digit number (#891)
The sum of the digits of a two-digit number is 13. The number is 27 more than the number formed by interchanging the tens digit with the one ...
systems of equations, systems, equations
- The sum of the reciprocals of two consecutive even integers (#2558)
The sum of the reciprocals of two consecutive even integers is 13/84...
fractional equations, equations
- The sum of the squares (#928)
The sum of the squares of two consecutive positive numbers is 61...
systems of equations, consecutive integers, solving equations, solving systems of equations, equations, systems, integers, number sense, numbers
- The sum of the squares of the two (#1053)
The sum of the squares of the two larger of three consecutive even integers is 12 less than 4 times the square of the smaller ...
polynomials, consecutive integers, solving systems of equations, systems of equations, solving equations, systems, equations, integers, number sense, numbers
- The sum of the squares of two consecutive (#1895)
The sum of the squares of two consecutive negative even integers is 100...
greatest common factor, solving equations, equations, systems, systems of equations, solving systems of equations
- The sum of the squares of two consecutive positive even integers (#2056)
The sum of the squares of two consecutive positive even integers is 244...
systems of equations, systems, equations
- The sum of three numbers (#3074)
The sum of three numbers is 15. The third number is nine less than the sum of the first and second number. The first number is four more than the third ...
systems of equations, systems, equations
- The sum of three numbers (#3112)
The sum of three numbers is 64. The second number is 3 more than the first. The third number is 11 less than twice the first. Find the numbers
equations
- The sum of two numbers (#1176)
The sum of two numbers is 20. Their difference is 4...
systems, systems of equations, equations
- The sum of two numbers (#264)
The sum of two numbers is 42. The difference is 14...
substitution method, solving quadratic equations, quadratic equations, solving equations, equations
- The sum of two numbers (#395)
The sum of two numbers is 26 and their difference is ...
substitution method, solving quadratic equations, quadratic equations, solving equations, equations
- The tallest structure in the U.S. (#341)
The tallest structure in the U.S. is a TV tower in Blanchard, North Dakota. Its height is 2063 feet. A 2382-foot length of wire is to be used as a guy wire attached to the top of the ...
radical equations, equations, radicals, numbers, number sense
- The total cost of a radio and a camera (#2374)
The total cost of a radio and a camera is $1650. If the radio costs 4/7 as much as the ...
fractions, numbers, fractional equations, equations, number sense
- The total proceeds from a used book sale (#3528)
The total proceeds from a used book sale were $115. A total of 65 books were sold. The books were priced at $1.50 and $2.00 each. How many books were sold for $1...
systems, solving systems of equations, systems of equations, equations, solving equations
- The width of a rectangular gate (#1824)
The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures 6 ...
equations, quadratic equations
- There are 48 heads and 134 legs (#1943)
There are 48 heads and 134 legs among the chicken and pigs on the ...
systems of equations, systems, equations
- There are a total of 126 cats and dogs (#2691)
There are a total of 126 cats and dogs at an animal shelter. For every 5 dogs, there are 4 ...
solving equations, systems, systems of equations, equations, solving systems of equations
- There are two phone plans (#3279)
There are two phone plans. One plan has $28 one time fee, and 9 cents a min. The second is 13 cents a ...
solving linear equations, linear equations, solving equations, equations
- There is a bag that contains (#1394)
There is a bag that contains: blue, green, and red marbles. There is a total value of 10 marbles. There are twice as many blue marbles as there are green, and the amount of red is one more than three times the amount of ...
equations, systems, systems of equations
- there is a ring of fourteen stepping stones (#2371)
there is a ring of fourteen stepping stones. A girl hops round the ring, stopping to change feet every time she has made three hops. She notices that when she has been round the ring three times, she has stopped to change feet on each one of the fourteen stones. The girl now hops round the ring, stopping to change feet every time she has made four hops. Explain ...
equations
- Three consecutive even integers (#1447)
Three consecutive even integers are such that the square of the third is 100 more than the square of the ...
consecutive numbers, consecutive integers, solving systems of equations, systems of equations, solving equations, systems, equations, integers, number sense, numbers
- Three pumps are being used to empty a small pool (#2611)
Three pumps are being used to empty a small pool. The first pump is twice as fast as the second pump. The first two pumps can empty the pool in 8 hours, while all three pumps can empty it in 6 hours. How long would it take each pump to empty the pool individually? Hint: Let x represent the fraction of the pool that the first pump can empty in one hour. Let y and z represent this fraction for the second and third ...
linear equations, equations
- Tickets for a school play cost (#1747)
Tickets for a school play cost $4 for adults and $2 for students. At the end of the play, the school sold a total of 105 tickets and collected $360. Write a linear system. Let x be the number of adult tickets sold and let y be the number of student tickets sold. Graph the ...
equations, systems, systems of equations
- Tickets to a movie cost (#1165)
Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75...
solving equations, solving systems of equations, systems, systems of equations, equations
- Tina hiked 15km up a mountain trail (#993)
Tina hiked 15km up a mountain trail. Her return trip along the same trail took 30 minutes less because she was able to increase her speed by 1km/...
fractional equations, equations
- Traci and Gene walk at the same rate (#2145)
Traci and Gene walk at the same rate and jog at the same rate.Traci walks for 1 hour and jogs for 1 hour, and covers a distance of 17km. Gene walks for 2 hours and jogs for half and hour, and covers a distance of 16...
systems of equations, systems, equations
- Trains at each end of the 50.0-km-long Eurotunnel (#3042)
Trains at each end of the 50.0-km-long Eurotunnel under the English Channel start at the same time into the tunnel. Find their speeds if the train from France travels 8.0 km/m faster than the train from England and they pass in 17...
equations
- Twice the sum of a number (#3006)
Twice the sum of a number and 9 is the same as 4 times the difference obtained when 6 is subtracted from the ...
equations
- Two cars started from the same point (#1751)
Two cars started from the same point but traveled in opposite directions. the faster car traveled 15 kilometers faster than the slower car. after five hours the 2 cars were 575 kilometers ...
linear equations, equations
- Two cows in four weeks can eat (#2304)
Two cows in four weeks can eat all of the grass on two acres and all the grass that grows on these two acres during the four weeks. Three cows in two weeks can eat all the grass on two acres and all the grass that grows on these two acres during the two weeks. How many cows can eat in six weeks all the grass on six acres and all the grass that grows on these six acres during the six ...
equations
- Two houses are for sale on the same street (#3503)
Two houses are for sale on the same street. The second house has 1000 square feet less than twice the square feet of the first house. Together the houseshave 4400 square ...
solving systems of equations, systems of equations, solving equations, systems, equations
- Two hundred tickets for the school play were sold (#3548)
Two hundred tickets for the school play were sold. Tickets cost $2.00 for students and $3 for adults. The total amount collected was $490.00...
equations, algebraic equations
- Two numbers are in the ratio (#864)
Two numbers are in the ratio 5:2. One half of their sum is 10 and a ...
fractional coefficients, expressions, algebraic fractions, algebraic expressions, algebraic equations, coefficients, equations
- Two numbers have a sum (#220)
Two numbers have a sum of 127. The larger is 17 more than the ...
solving equations, equations
- Two rental airplanes were flown (#2169)
Two rental airplanes were flown a total of 54 hours in one month. One plane rents for $105/h, and the other rents for $130/h. The total income from the two planes was $6570...
systems of equations, systems, equations, solving systems of equations, solving equations
- Two satellites are orbiting earth (#250)
Two satellites are orbiting earth. The path of one has the equation x2 +y2 = 2250000. The orbit of the other is 200 km farther fro the centre of earth. In one ...
circle equation, circles, equations, plane figures, shapes, curves
- Two taps turned on together (#1286)
Two taps turned on together can fill a tank in 15 mins. Separately, one tap takes 16mins longer than the other tap to fill the ...
solving rational equations, solving equations, equations, rational equations, work rate, rate
- What number must be added to both the numerator and the denominator (#2419)
What number must be added to both the numerator and the denominator of the fraction 5/11 to make the result equal 5/9?
fractional equations, equations
- What value of c makes (#2990)
What value of c makes x2-x+c a perfect square?
completing the square, solving quadratic equations, quadratic equations, solving equations, equations
- Write a mathematical expression for each number (#3161)
Write a mathematical expression for each number 1 through 18, using only the number 4 and mathematical symbols. The goal is to use the fewest number of 4s as possible. No other digit can be used. NOTE: Fours can be combined to create 44, 4.4, 444, 0.4...
quadratic equations, equations
- You are selling tickets for a high school basketball game (#1127)
You are selling tickets for a high school basketball game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect $1450...
substitution method, solving quadratic equations, quadratic equations, solving equations, equations
- You are selling tickets to a high school play (#2760)
You are selling tickets to a high school play. Student tickets cost $5 and general admission tickets cost $8. you sell 566 tickets and collect $3797...
solving equations, equations, solving systems of equations, systems of equations, systems
- You have made a quilt (#522)
You have made a quilt that is 4 feet by 5 feet. You want to use the remaining 10 square feet as a decorative border of uniform ...
solving quadratic equations, completing the square, quadratic equations, solving equations, equations
- You want to build a fence around a square garden (#2917)
You want to build a fence around a square garden that covers 506.25ft2...
quadratic equations, equations
- You want to put a fence around your vegetable garden (#396)
You want to put a fence around your vegetable garden. The garden has a square shape. You want the fence to be one yard away from each side of the garden. You used 56 yards of ...
literal equations, equations
