Algebra 1 Practice Test: Linear Equation Word Problems
- Linear Equation Word Problems
- 10 questions
- 15 minutes
These 10 questions ask you to turn a situation into a linear equation and solve it. Tip: define the variable first, then check your answer against the words of the problem.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
The sum of three consecutive integers is 87. What is the smallest of the three?
Correct answer: B
Let the integers be n, n + 1 and n + 2. Then 3n + 3 = 87, so n = 28 (28 + 29 + 30 = 87). The answer 29 is the middle number.
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Question 2
The sum of two consecutive odd integers is 64. What is the larger integer?
Correct answer: D
Let them be n and n + 2. Then 2n + 2 = 64, so n = 31 and the larger one is 33. 32 is even, so it cannot be one of them.
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Question 3
The length of a rectangle is 3 meters more than twice its width. The perimeter is 54 meters. What is the length?
Correct answer: A
With width w: 2(w + 2w + 3) = 54, so 6w + 6 = 54 and w = 8. The length is 2(8) + 3 = 19 meters; 8 is the width.
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Question 4
Two cars leave the same place at the same time and drive in opposite directions, one at 55 mph and the other at 65 mph. After how many hours are they 360 miles apart?
Correct answer: C
Moving apart, their distances add: 55t + 65t = 360, so 120t = 360 and t = 3. Using the average speed 60 for the total distance gives the wrong 6 hours.
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Question 5
Phone plan A costs $20 per month plus $0.10 per minute. Plan B costs $35 per month with unlimited minutes. For how many minutes do the plans cost the same?
Correct answer: B
20 + 0.10m = 35, so 0.10m = 15 and m = 150. Using more than 150 minutes makes plan B cheaper.
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Question 6
How many liters of a 20% acid solution must be added to 10 liters of a 50% acid solution to make a 30% acid solution?
Correct answer: D
Acid amounts: 0.20x + 0.50(10) = 0.30(x + 10). So 0.20x + 5 = 0.30x + 3, which gives 0.10x = 2 and x = 20. Check: 4 + 5 = 9 liters of acid in 30 liters is 30%.
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Question 7
Maria is 4 times as old as her son. In 20 years, she will be twice as old as he will be. How old is her son now?
Correct answer: A
Son s, Maria 4s. In 20 years: 4s + 20 = 2(s + 20), so 2s = 20 and s = 10. 40 is Maria's age now.
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Question 8
A jar holds 30 coins, all dimes and quarters, worth $5.10 in total. How many quarters are in the jar?
Correct answer: C
With d dimes: 0.10d + 0.25(30 − d) = 5.10, so 7.50 − 0.15d = 5.10 and d = 16. That leaves 14 quarters ($1.60 + $3.50 = $5.10).
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Question 9
"Five less than three times a number is 22." Which equation matches this sentence?
Correct answer: B
"Three times a number" is 3n, and "five less than" it means subtract 5 from 3n: 3n − 5. Writing 5 − 3n reverses the order.
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Question 10
A tank holds 500 gallons of water and drains at 12 gallons per minute. After how many minutes will 140 gallons be left?
Correct answer: D
500 − 12t = 140, so 12t = 360 and t = 30 minutes.
Questions you leave blank are not counted as wrong.
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