Algebra: Equations Word Problems
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Algebra: Equations WordProblems
Erica hiked up a mountain trial
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 ...
A circle with radius 5
A circle with radius 5 has its center at (4,1). the line x-2y+4=0 intersects the circle. find the intersections
Crane A can unload the container ship
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....
If a ladder is leaning against a building
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 ...
A bike shop rents mountain bikes
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...
Two satellites are orbiting earth
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 ...
The area of a triangle
The area of a triangle is 30in
2. The base of the triangle measures 2 in. more than twice the height of the ...
At the afternoon matinee movie
At the afternoon matinee movie 3 adult tickets and 4 child tickets cost $41, and 4 adult tickets and 3 child tickets cost $43...
completing the square
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= -0.002d
2 + 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 ...
A ball is shot into the air
A ball is shot into the air. It's height , h in metres after t seconds is modeled by h=-4.9t
2 + 30t +1.6...
Sarah had an idea
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 ...
A motor boat travels
A motor boat travels 400km. If the boat went 18km/h faster, it could have traveled 600 km in the same amount of ...
Two taps turned on together
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 ...
Andres and Biloy working together
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 ...
A town`s old street sweeper
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 ...
Bob, driving a new Ford
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 ...
A model rocket is shot into the air
A model rocket is shot into the air and its path is approximated by h = -5t
2 + 30t where h is the height of the rocket above the ground in metres and t is the elapsed time in ...
A software development company is getting ready
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 ...
The board of directors of a corporation
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 ...
A rectangular garden is 5 feet longer
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 ...
A rectangular lot whose perimeter
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...
A framer at a photo gallery
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 ...
The tallest structure in the U.S.
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 ...
How do the Quarter Pounder and Whopper
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 ...
You have made a quilt
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 ...
Suppose you invest $2000 today
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 ...
Mark bought 114 meters of fencing
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 ...
Frank`s Specialty Coffees makes
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...
My friends and I went to the mall
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...
There are two phone plans
There are two phone plans. One plan has $28 one time fee, and 9 cents a min. The second is 13 cents a ...
9 times the side of one square exceeds
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 ...
The band boosters are organizing a trip
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 ...
Suppose you decide to move your garden
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 ...
A bulldozer can move 25 tons/h of material
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...
Ahmed has first half of a treasure map
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 ...
A boat traveled 126 miles
A boat traveled 126 miles downstream and back. The trip downstream took 6 hours. The trip back took 42 ...
I bought a can of varnish
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 ...
The height of a batted baseball as a function of time
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 ...
The owner of a health foods store
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 ...
It costs $5 to become a new member
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...
A cricket jumps off the ground
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.
...
A chemical plant is rectangular and has a length
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 ...
Tickets to a movie cost
Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75...
A parallelogram has a base
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)
Flex drove 800 miles in x hours
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 ...
The total proceeds from a used book sale
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...
Rudy must play 12 commercials
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 ...
The side of a square house is 24 ft long
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 ...
Two houses are for sale on the same street
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 ...
Two rental airplanes were flown
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...
The length of a rectangle is 2 feet more
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)
Tasty Bakery sells three kinds of muffins
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 ...
A candy shop sells two new flavors of candy
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 ...
midpoint
If ab=6, bc=9 and ac=13, what must be true of points a,...
A boy walked at the rate
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 ...
A community center sells
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 ...
A total of 512 tickets were sold
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 ...
A grocer plans to mix candy
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 ...
Danny had $22.00 in loonies and toonies
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 ...
The following table gives the population
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 ...
A mixture of 12 liters of chemical A
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 ...
Diophantus was a famous Greek mathematician
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 ...
Dave sold popcorn and pretzels
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 ...
A motorcycle breaks down and the rider
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 ...
Two cars started from the same point
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 ...
At full speed, an airplane can travel
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 ...
Tina hiked 15km up a mountain trail
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/...
Three pumps are being used to empty a small pool
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 ...
systems of equations
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 ...
A machine produces open boxes
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 ...
Find a two-digit number
Find a two-digit number where the sum of the digits is 6 and the number is 6 times the unit's digit.
copper that was 63% pure
copper that was 63% pure was melted together with copper that was 90% pure to make 18 kilograms of an alloy that was 75% ...
The population of black mountain
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 ...
A child in an airport is able to cover
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 ...
During a used book sale
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
The sum of three numbers
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 ...
The chief executive has just requested
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...
A total of 50 juniors and seniors
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...
Tickets for a school play cost
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 ...
There is a bag that contains
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 ...
A man buys x cans of beer
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...
A piggy bank contains 20 coins
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...
Traci and Gene walk at the same rate
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...
Rudy must play 12 commercials
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 ...
A supplier gives a quote for you
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)...
Write a mathematical expression for each number
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...
At the animal shelter
At the animal shelter there were 46 cats and dogs. There were 18 more dogs than ...
Two cows in four weeks can eat
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 ...
The sum of three numbers
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
Bob, traveling in a new Ford
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 ...
Ahmed has half of a treasure map
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 ...
Twice the sum of a number
Twice the sum of a number and 9 is the same as 4 times the difference obtained when 6 is subtracted from the ...
Trains at each end of the 50.0-km-long Eurotunnel
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...
there is a ring of fourteen stepping stones
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 ...
The restaurant can currently seat 120 people
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 ...
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