- 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 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 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 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 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 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 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 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 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 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 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
- 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
- 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
- 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
- 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 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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 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 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 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 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 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 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 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
- 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
- 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
- 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
- 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 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 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 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
- 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
