Name
Date
Period
Applications of Linear Equations
For each of the following word problems, setup an equation that can be used to model the
given situation. Then solve the equation. If necessary, make sure to answer the question
being asked.
1. Six times a certain number plus 11 is 35. What is the number?
2. Five more than twice a number is three more than four times the number. What is the
number?
3. Twenty-one less than three times a number is five more than the number. What is the
number?
4. Find three consecutive integers whose sum is 96.
5. Find three consecutive odd integers whose sum is -15.
6. The sum of three consecutive integers is 279. Find the integers.
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Date
Period
7. The sum of two consecutive odd integers is 112. Find the integers.
8. Find four consecutive integers such that the sum of the second and fourth is 132.
9. The second of two numbers is 3 less than twice the first. Their sum is 36. Find the first
number.
10. The smaller of two numbers is 30 less than three times the larger. The sum of the numbers is
22. Find the numbers.
11. Three numbers are such that the second number is 6 less than twice the first number, and the
third number is five more than the sum of the first two. The sum of the numbers is 293. Find
the numbers.
12. Two consecutive even integers are such that twice the first, plus three times the second, is
equal to 156. Find the numbers.
Name
Date
Period
13. Three consecutive integers are such that the first, plus twice the second, plus three times the
third is equal to 200. Find the numbers.
14. The second side of a triangle is twice the first side and the third side is 10 more than the
second side. The perimeter of the triangle is 70 feet. Find the sides of the triangle.
15. The length of a rectangle is 5 meters more than twice the width. The perimeter is 130 meters.
Find the dimensions of the rectangle.
16. The width of a rectangle is 50 feet less than the length. If the perimeter is 400 feet, find the
length and width of the rectangle.
17. The temperature at 8:00 am was 35. Every hour, the temperature fell 2.5. How many
hours did it take for the temperature to reach -5?
18. Mrs. Cote’s washing machine needs to be fixed. Since her machine is pretty old, she does
not want to spend more than $100 for repairs. A service call will cost $35, and the labor will
be an additional $20 per hour. What is the maximum number of hours that the repair person
can work and keep the total cost at $100?
Name
Date
Period
19. Nilka bought a winter coat for $6 less than half its original price. Nilka paid $65 for the coat.
What was the original price?
20. Adam started a savings account by depositing $150. Each week he plans to deposit $18.
How many weeks will it take him to reach a total of $500 in the account?
21. The state fair charges $6.00 for admission plus $2.25 for each ride. Zach has $25 to spend.
How many rides can he take?
22. The gasoline tank on Cynthia’s car holds 13 gallons of gas. The car uses 351 gallon of
gasoline for every mile that Cynthia drives it. The car’s fuel light comes on when there are 3
gallons of gas left in the tank. How many miles can Cynthia drive the car before the light
comes on?
23. At the U-Pick Strawberry Farm, Elise paid a total of $5.59. She paid $.55 for an empty
basket and $.48 a pound for the strawberries she picked. How many pounds of strawberries
did she pick?
24. A printer prints at a rate of 6 pages per minute. Suppose the printer starts with 1100 sheets of
paper. After how many minutes will 350 sheets be left?
Name
Date
Period
25. There is $150 in a fund for a school dance. Tickets will be sold for $4.50 each. How many
persons must attend the dance in order to cover the estimated expenses of $400?
26. A local tow-truck company charges a service fee of $25 for each tow that it performs. In
addition, they charge $.75 per mile that the vehicle is towed. If the total for a bill was $58,
how many miles was the car towed?
27. Matt presently weighs 260 pounds. He wants to weigh 190 lbs in 26 weeks. To obtain his
goal, how much weight must he lose per week?
28. Katana works at a nearby restaurant and earns $8.30 an hour. In one night, she earned $45 in
tips. All together (salary and tips), she earned $78.20. How many hours did she work?
29. Columbus, Ohio had a population of 565,000 people, which had been increasing at an
average rate of 2500 people per year. Milwaukee, Wisconsin’s population was 636,000, but
was decreasing at a rate of 8000 people per year. If the rates continued, in how many years
will the populations of the two cities be the same?
30. Alaska has a population of 480,000, which has been increasing at a rate of 6000 people a
year. Delaware’s population of 606,000 has been increasing at a rate of 4000 people per
year. If the rates of increase do not change, in how many years will the populations be
equal?
Name
Date
Period
31. Jaida has $20 and is saving at a rate of $6 per week. Her brother, J. J, has $150, but is
spending at a rate of $8 a week. After how many weeks will each have the same amount of
money?
32. In 1988, the women’s world record for the 100-m freestyle in swimming was 54.73 seconds.
It had been decreasing at a rate of 0.33 seconds per year. The men’s record was 49.36
seconds and has been decreasing at 0.18 seconds a year. Assuming that the rates continued,
how many years after 1988 would the records have been the same?
33. A tank that contains 340 gallons of water is being drained at a rate of 15 gallons per hour.
Another tank, which starts with 60 gallons, is being filled at a rate of 20 gallons per hour.
After how many hours will they both hold the same amount?
34. Alex has $105 and spends $10 every week. Steven has $45 and saves 5 dollars every week.
In how many weeks will they have the same amount of money?
35. The Saulnier family wants to rent a truck for a day. They have a choice of two rental
companies. Company A charges $30 per day plus $.60 per mile and Company B charges $55
per day plus $.35 per mile. The family would like to know after how many miles are the
total costs of the two companies the same.