Grade 8 Word Problems: Writing and Solving Linear Equations
Grade 8 word problems that set up and solve linear equations — gym fees, taxi fares, consecutive integers. Fourteen problems with worked answers.
Solve each equation and answer the question. Show the steps that isolate the variable.
- 1.A gym charges a $25 sign-up fee plus $15 per month. The equation 15m + 25 = 145 gives the number of months m for a $145 total. Solve for m.
- 2.A taxi charges $3.00 plus $2.50 per mile. The equation 2.5x + 3 = 23 models a $23.00 fare. How many miles x was the ride?
- 3.Two consecutive integers add to 47. The equation x + (x + 1) = 47 models this. What is the smaller integer x?
- 4.A number is decreased by 3, then the result is multiplied by 4 to give 20. Solve 4(x - 3) = 20.
- 5.Two phone plans cost the same at x minutes. Solve 5x + 8 = 3x + 20 to find x.
- 6.A rectangle is 3 cm longer than it is wide, and its perimeter is 26 cm. Solve 2(w + 3) + 2w = 26 for the width w.
- 7.Solve 2(x + 4) = 3x - 1 to find the number x that makes both expressions equal.
- 8.A number tripled and then decreased by 7 equals 26. Solve 3x - 7 = 26.
- 9.Two trucks carry equal loads. Solve 6x - 4 = 2x + 16 to find the load x in tons.
- 10.Plan A costs $30 plus $0.10 per minute; Plan B costs a flat $50. Solve 0.1x + 30 = 50 for the number of minutes x where the plans cost the same.
- 11.The temperature falls at a steady rate. Solve -3x + 12 = 3 to find the number of hours x.
- 12.Solve 7 - 2x = -5 for x.
- 13.Two angles measuring x and 2x degrees are complementary, so they add to 90. Solve x + 2x = 90.
- 14.A tank holds 6 liters and is filled at half a liter per minute to reach 14 liters. Solve 0.5x + 6 = 14 for the minutes x.
What this worksheet covers
This is a 14-problem sheet — one page to work through, one page of answers to check against. Two of the fourteen problems involve a negative quantity, so the answer is not always larger than what went in; the problems are written as situations, so a student has to translate before they can calculate. It is written against Common Core 8.EE.7 — part of Expressions & Equations in grade 8.
Skills practiced
At this point in the sequence, work in word problems is really about percent, proportion, and algebraic modeling. Concretely, the page tests whether a student can read a situation and choose an operation before computing, keep decimal points aligned rather than right-aligning digits out of habit, and track direction as well as magnitude. Fluency, not just correctness, is the target here — accurate and unhurried is the mark to aim for.
How to use this worksheet
Expect this to take twenty minutes or so of genuine attention. At grade 8, work in word problems rewards care over speed — a student who rushes it will get the arithmetic right and the signs wrong. Ask the student to re-work one missed problem from scratch rather than correcting the answer in place — the second attempt shows whether the method changed.
One mistake to watch for
Percent increase is computed against the wrong base: 20% off $50 then 20% back on returns to $50.
The percent is being applied to whichever number is nearest rather than to the stated base.
Name the base out loud before every percent computation. The second 20% is 20% of $40, not of $50 — which is why the price does not come back.
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- Grade 7 Percent, Tax, Tip, and Discount Word Problems — grade 7, 14 problems
No sign-up and no paywall — download the word problems sheet, print it, and the answers for all fourteen problems are on the page behind it.