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.
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Three different problem sets — same skill, same layout, fresh numbers.
Preview — Set A
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 word problems for grade 8 expressions and equations, printed in black and white with the key on page two. What makes this set particular: two of the fourteen problems involve a negative quantity and the problems are written as situations that have to be translated before they can be calculated. Problems 5 and 10, for instance, are "Two phone plans cost the same at x minutes. Solve 5x + 8 =…" and "Plan A costs $30 plus $0.10 per minute; Plan B costs a flat…". The sheet sits inside Common Core 8.EE.7, in the grade 8 Expressions & Equations strand.
Skills practiced
The grade 8 expressions and equations sequence covers multi-step linear equations, operations in scientific notation and integer exponent rules; this page sits inside it. The skill on the page: grade 8 Word Problems: Writing and Solving Linear Equations. Working the page asks a student to read a situation and choose an operation before computing, keep the decimal points aligned, and track direction as well as magnitude. Twelve different answers appear across the fourteen problems, so a student cannot copy one result down the page.
About the word problems format
The 14 story problems each get a full line and an answer rule; problem 5, "Two phone plans cost the same at x minutes. Solve 5x + 8 =…" is one of them. Translating a sentence into an equation is the skill the drill sheets cannot practice, and the one that matters most.
Set A, Set B and Set C
Set A is the original sheet; Sets B and C redraw each problem with the same shape and recomputed answers. Where Set A's problem 8 is "A number tripled and then decreased by 7 equals 26. Solve…", Set B's is "The temperature falls at a steady rate. Solve -4x + 15 = -5…".
13 story problem(s) drawn from the 8.EE.7 context family (linear equations in one variable) — parameters inferred from the standard and grade
How to use this worksheet
Work it without a calculator. Every one of the fourteen expressions and equations problems is designed to be done by hand, and reaching for a calculator at grade 8 skips exactly the reasoning being built. If more than a third of the fourteen problems come back wrong, stop and step back a grade in expressions and equations rather than assigning Set B.
One mistake to watch for
The distributive property only reaches the first term: 3(x + 4) is expanded to 3x + 4 instead of 3x + 12. Problem 7 on this grade 8 word problems page, "Solve 2(x + 4) = 3x - 1 to find the number x that makes…", is where to look for it.
The multiplier is being attached to the nearest term only.
Draw arrows from the multiplier to each term inside the bracket before writing anything.
Other grade 8 expressions and equations formats
The same skill in the other formats available at this grade.
A step either side
The same format one grade down and one grade up — the easier sheet is often the faster fix when this one is not landing.
- 7.EE.4 — Equations & Inequalities in the Real World — grade 7, 22 problems
Word Problems sheets in other grade 8 topics
Print as many copies of this grade 8 expressions and equations word problems as you need; Sets A, B and C and their keys are six separate PDFs, all free.