Appendix B: Sample Word Problems
A. One Variable (1 unknown)
1. One-Step Equations
a. A 40- ft rope is cut into 2 pieces. One piece is 4 ft, what is the length of the other piece?
b. The length of a rope is reduced by 10 feet. Now the rope is 100 feet in length. What is the length of the original rope?
c. The length of a rope is 100 feet and is cut into 5 equal pieces. What is the length of one piece?
d. The average length of 5 pieces of rope is 20 feet. What is the total length of all 5 pieces?
e. In the 2004 Olympics, Shawn Crawford won the 200 meter dash. His winning time was 19.79 seconds. Find his average speed to the nearest tenth of a meter per second.
f. In Everglades National park in Florida, there are 200 species of birds that migrate. This accounts for 4/7 of all the species of birds sighted in the park. Find the number of species of birds that have been sighted in Everglades National Park.
2. Two-Step Equations
a. A 9- ft rope is cut into 2 pieces so that one piece is twice the other. How long is each piece?
b. Two ropes are together 275 yards long. One rope is 50% longer than the other. How long are the ropes?
c. How old am I if 400 reduced by 2 times my age is 244?
d. How old am I if 40 increased by 3 times my age is 100?
e. Jill sold half of her comic books and then bought 16 more. She now has 36. With how many did she begin?
f. Jill sold ¾ of her comic books and then gave her friend 2 of them. She now has 100. With how many did she begin?
g. John has three sacks of apples and three more in his pocket. Each sack contains the same number of apples. Altogether he has 33 apples. How many apples are in each sack?
h. Kim has a job where she makes $8 per hour plus tips. Yesterday, Kim made $53 dollars, $13 of which was from tips. How many hours did she work?
i. Tyler paid $124 to get his car repaired. The total cost for the repairs was the sum of the amount paid for parts and the amount paid for labor. Tyler was charged $76 for parts and $32 per hour for labor. Find the amount of time it took to repair his car.
j. A skateboarding park charges $7 per session to skate and $4 per session to rent safety equipment. Jared rents safety equipment every time he skates. During one year, he spends $99 for skating charges and equipment rentals. How many sessions did Jared attend?
k. the capacity of a landfill is 4,756,505 tons. The landfill currently holds 2,896,112 tons. A cell is added to the landfill everyday, and each cell averages 1600 tons. After how many days will the landfill reach capacity? Round your answer to the nearest day.
3. Multi-Step Equations
a. A 10- ft long piece of wood is cut into 2 pieces so that 1 piece is 2 feet longer than the other. What is the length of the two pieces?
b. A length of a board was 10 inches shorter than another length. Together the boards were 20 inches. How long were the boards?
c. A 12-ft rope is cut into 3 pieces so that the second piece is 1 foot longer than the first and the third piece is 1 foot longer than the second. How long is each piece?
d. An 80 inch board is to be cut into 3 pieces so that 1 piece is twice another and the third piece is 10 inches more than the second. Find the length of each piece.
e. A pile of 18 coins consists of quarters and dimes. If the total amount of the coins is $3.00, find the number of quarters and dimes the child has.
f. A small child has 6 more quarters than nickels. If the total amount of the coins is $3.00, find the number of nickels and quarters the child has.
g. A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
h. A person has quarters and dimes that total $2.80. The number of dimes is 7 more than the number of quarters. How many of each coin does the person have?
i. The length of a rectangle is 3.5 inches more than its width. The perimeter of the rectangle is 31 inches. Find the length and the width of the rectangle.
j. A ticket agency sells tickets to a professional basketball game. The agency charges $32.50 for each ticket, a convenience charge of $3.30 for each ticket, and a processing fee of $5.90 for the entire order. The total charge for an order is $220.70. How many tickets were purchased?
k. A roofing contractor gives estimates for shingling a roof in cost per square, where a square is a 10 foot by 10 foot section of roof. The contractor estimates $27.50 per square for materials, $17 per square for labor, $30 per square for overhead and profit, and a total of $750 for miscellaneous expenses. If the contractor gives an estimate of $2314.50, about how many squares does the roof have?
4. Mixture Problems
a. How much cream that is 20% butterfat should be mixed with milk that is 5% butterfat to get 10 gallons of cream that is 14% butterfat?
b. How much of a solution that is 18% fertilizer must be mixed with a solution that is 30% fertilizer to get 50 gallons of a solution that is 27% fertilizer?
c. A candy store owner wants to make 30 one-pound boxes of candy costing $5.00 a box. If she wishes to use 12 pounds of candy costing $8.00 per pound, what should be the cost of the other type of candy she should use?
d. How much of a 10% vinegar solution should be added to 2 cups of a 30% vinegar solution to make a 20% solution?
B.Simultaneous Equations (2 unknowns)
1. Different Values/Percentage
a. You are selling tickets for a musical at your local community college. Student tickets cost $5 and general admission tickets cost $8. If you sell 500 tickets and collect $3475, how many student tickets and how many general admission tickets are sold?
b. You are selling tickets to a concert. Student tickets cost $1.25 and adults cost $2.25. If you sell 560 tickets and collect $916, how many student tickets were sold?
c. Ed invested $2000, one part at 3% interest and one part at 1.5% interest. If he got $41.25 simple interest in one year, how much did he invest at each percentage?
d. Paul invested $3000, part in a 1-year CD paying 1.20% and the rest in municipal bonds that pay 3% a year. The annual return from both accounts was $72. How much was invested in bonds?
e. Margie is responsible for buying a week's supply of food and medication for the dogs and cats at a local shelter. The food and medication for the dogs cost twice as much as those supplies for the cats. She needs to feed 164 cats and 24 dogs. Her budget is $4240. How much can she spend on dogs?
f. A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $487. The second order was for 6 bushes and 2 trees, and totaled $232. The bill does not list the per-item price. What is the cost of one bush and of one tree?
g. A passenger jet took 3 hours to fly 1800 miles in the direction of the jet stream. The return trip against the jet stream took 4 hours. What were the jet's speed in still air and the jet stream's speed?
h. You just purchased a cellular phone and are trying to decide the best cellular phone company in which to give your business. When you contacted the Talks-A-Lot company, they were offering a monthly plan of $40 for 500 minutes and $0.25 for each minute over the 500 minutes. Chat - Away is charging $35 for 500 minutes and $0.30 for each additional minute over 500. How many minutes would you have to talk over the 500 minutes for the cost to be the same with both companies? What would be the equal cost?
i. Dan and Sydney are getting high-speed Internet access at the same time. Dan's provider charges $60 for installation and $42.95 per month. Sydney's provider has free installation and charges $57.95 per month. After how many months will Dan and Sydney have paid the same amount for high-speed Internet service?
k. For $360, a rock-climbing gym offers a yearly membership where members can climb as many days as they want and pay $4 per day for equipment rental. Nonmembers pay $10 per day to use the gym and $6 per day for equipment rental. Find the number of visits after which the total cost for a member and the total cost for a nonmember are the same.
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