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 practised
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, and the answer key writes the unit with every answer. Translating a sentence into an equation is the skill the drill sheets cannot practise, and the one that matters most.
Set A, Set B and Set C
Set A is the sheet as it was first published on MathSheetLab, and Sets B and C were derived from it problem by problem: each number became a slot redrawn with the same shape, and every answer was recomputed exactly. 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 same operation is not done to both sides: x + 5 = 12 becomes x = 12 + 5. Problem 10 on this grade 8 word problems page, "Plan A costs $30 plus $0.10 per minute; Plan B costs a flat…", is where to look for it.
The equation is being read as instructions rather than as a balance.
Draw a line down through the equals sign and write the inverse operation on both sides of it, every time.
Other grade 8 expressions and equations formats
The same skill in the other formats available at this grade.
- Drill — Grade 8 Adding Numbers in Scientific Notation, 16 problems
- Timed Drill — 8.EE.3 — Scientific Notation Division Practice, 22 problems
- Missing Number — Grade 8 Expressions & Equations Missing Number, 24 problems
- Mixed Review — Grade 8 Subtracting Numbers in Scientific Notation, 16 problems
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.