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# Algebra Word Problems Practice Questions Set 3

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## Algebra Word Problems

Basic algebra problems ask you to solve equations in which one or more elements are unknown. The unknown quantities are represented by variables, which are letters of the alphabet, such as x or y. The questions in this set of practice problems give you practice in writing algebraic equations and using these expressions to solve problems.

1. The sum of two consecutive odd integers is –112. What is the larger integer?
1. –55
2. –57
3. 55
4. 57
2. The sum of three consecutive even integers is 114. What is the value of the largest consecutive integer?
1. 36
2. 34
3. 40
4. 38
3. Two commuters leave the same city at the same time but travel in opposite directions. One car is traveling at an average speed of 63 miles per hour, and the other car is traveling at an average speed of 59 miles per hour. How many hours will it take before the cars are 610 miles apart?
1. 4
2. 6
3. 30
4. 5
4. Two trains leave the same city at the same time, one going east and the other going west. If one train is traveling at 65 mph and the other at 72 mph, how many hours will it take for them to be 822 miles apart?
1. 9
2. 7
3. 8
4. 6
5. Two trains leave two different cities 1,029 miles apart and head directly toward each other on parallel tracks. If one train is traveling at 45 miles per hour and the other at 53 miles per hour, how many hours will it take before the trains pass?
1. 9.5
2. 11
3. 11.5
4. 10.5
6. Nine minus five times a number, x, is no less than 39. Which of the following expressions represents all the possible values of the number?
1. x ≤ 6
2. x ≥ –6
3. x ≤ –6
4. x ≥ 6
7. Will has a bag of gumdrops. If he eats 2 of his gumdrops, he will have between 2 and 6 of them left. Which of the following represents how many gumdrops, x, were originally in his bag?
1. 4 < x < 8
2. 0 < x < 4
3. 0 > x > 4
4. 4 > x > 8
8. The value of y is between negative three and positive eight inclusive. Which of the following represents y?
1. –3 ≤ y ≤ 8
2. –3 < y ≤ 8
3. –3 ≤ y < 8
4. –3 ≥ y ≥ 8
9. Five more than the quotient of a number and 2 is at least that number. What is the greatest value of the number?
1. 7
2. 10
3. 5
4. 2
10. Carl worked three more than twice as many hours as Cindy did. What is the maximum amount of hours Cindy worked if together they worked 48 hours at most?
1. 17
2. 33
3. 37
4. 15
11. The cost of renting a bike at the local bike shop can be represented by the equation y = 2x + 2, where y is the total cost and x is the number of hours the bike is rented. Which of the following ordered pairs would be a possible number of hours rented, x, and the corresponding total cost, y?
1. (0, –2)
2. (2, 6)
3. (6, 2)
4. (–2, –6)
12. A telephone company charges \$.35 for the first minute of a phone call and \$.15 for each additional minute of the call. Which of the following represents the cost y of a phone call lasting x minutes?
1. y = 0.15(x – 1) + 0.35
2. x = 0.15(y – 1) + 0.35
3. y = 0.15x + 0.35
4. x = 0.15y + 0.35
13. A ride in a taxicab costs \$1.25 for the first mile and \$1.15 for each additional mile. Which of the following could be used to calculate the total cost y of a ride that was x miles?
1. x = 1.25(y – 1) + 1.15
2. x = 1.15(y – 1) + 1.25
3. y = 1.25(x – 1) + 1.15
4. y = 1.15(x – 1) + 1.25
14. The cost of shipping a package through Shipping Express is \$4.85 plus \$2 per ounce of the weight of the package. Sally only has \$10 to spend on shipping costs. Which of the following could Sally use to find the maximum number of ounces she can ship for \$10?
1. 4.85x + 2 ≤ 10
2. 4.85x + 2 ≥ 10
3. 2x + 4.85 ≤ 10
4. 2x + 4.85 ≥ 10
15. Green Bank charges a monthly fee of \$3 for a checking account and \$.10 per check. Savings-R-Us bank charges a \$4.50 monthly fee and \$.05 per check. How many checks need to be used for the monthly costs to be the same for both banks?
1. 25
2. 30
3. 35
4. 100
16. Easy Rider taxi service charges a pick-up fee of \$2 and \$1.25 for each mile. Luxury Limo taxi service charges a pick-up fee of \$3.25 and \$1 per mile. How many miles need to be driven for both services to cost the same amount?
1. 24
2. 12
3. 10
4. 5
17. The sum of two integers is 36, and the difference is 6. What is the smaller of the two numbers?
1. 21
2. 15
3. 16
4. 18
18. One integer is two more than another. The sum of the lesser integer and twice the greater is 7. What is the greater integer?
1. 1
2. 2
3. 3
4. 7
19. One integer is four times another. The sum of the integers is 65. What is the value of the lesser integer?
1. 42
2. 64
3. 30
4. 13
20. The sum of three times a greater integer and 5 times a lesser integer is 9. Three less than the greater equals the lesser. What is the value of the lesser integer?
1. 0
2. 1
3. 2
4. 3
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