Year 8 Equation Word Problems Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 8 linear equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Linear EquationsYear 8 Equation Word Problems Worksheet — Level 2 — Practice Set 4 — Answers
For each problem, choose a letter for the unknown, write an equation, solve it, and check your answer in the words of the problem.
1.A rectangle is 2 cm longer than it is wide. Its perimeter is 60 cm. Find its width and length.
Answer: width 14 cm, length 16 cm
- 2(w + w + 2) = 60
- 4w + 4 = 60
- w = 14, so length = 16
2.Layla thinks of a number, subtracts 6 and multiplies the result by 3. The answer is 51. What was the number?
Answer: 23
- 3(n − 6) = 51
- n − 6 = 17
- n = 23
3.A rectangle is 3 cm longer than it is wide. Its perimeter is 14 cm. Find its width and length.
Answer: width 2 cm, length 5 cm
- 2(w + w + 3) = 14
- 4w + 6 = 14
- w = 2, so length = 5
4.Archie thinks of a number, multiplies it by 4 and then adds 8. The answer is 40. Write an equation and find the number.
Answer: 8
- Let the number be n: 4n + 8 = 40
- 4n = 32
- n = 8
5.The sum of 3 consecutive whole numbers is 84. Find the numbers.
Answer: 27, 28, 29
- n + (n + 1) + (n + 2) = 84
- 3n + 3 = 84
- n = 27
6.Layla thinks of a number, multiplies it by 6 and then adds 14. The answer is 116. Write an equation and find the number.
Answer: 17
- Let the number be n: 6n + 14 = 116
- 6n = 102
- n = 17
7.Jayden thinks of a number, subtracts 9 and multiplies the result by 2. The answer is 6. What was the number?
Answer: 12
- 2(n − 9) = 6
- n − 9 = 3
- n = 12
8.A rectangle is 4 cm longer than it is wide. Its perimeter is 68 cm. Find its width and length.
Answer: width 15 cm, length 19 cm
- 2(w + w + 4) = 68
- 4w + 8 = 68
- w = 15, so length = 19
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.