Year 8 Equation Word Problems Worksheet — Level 3 — 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 3 — 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 1 cm longer than it is wide. Its perimeter is 46 cm. Find its width and length.
Answer: width 11 cm, length 12 cm
- 2(w + w + 1) = 46
- 4w + 2 = 46
- w = 11, so length = 12
2.The sum of 3 consecutive whole numbers is 177. Find the numbers.
Answer: 58, 59, 60
- n + (n + 1) + (n + 2) = 177
- 3n + 3 = 177
- n = 58
3.Mason buys some notebooks at $4.50 each and pays $8.00 for delivery. The total is $21.50. How many notebooks did Mason buy?
Answer: 3
- 4.50n + 8.00 = 21.50
- 4.50n = 13.50
- n = 3
4.Mason buys some notebooks at $3.50 each and pays $3.00 for delivery. The total is $24.00. How many notebooks did Mason buy?
Answer: 6
- 3.50n + 3.00 = 24.00
- 3.50n = 21.00
- n = 6
5.A rectangle is 1 cm longer than it is wide. Its perimeter is 70 cm. Find its width and length.
Answer: width 17 cm, length 18 cm
- 2(w + w + 1) = 70
- 4w + 2 = 70
- w = 17, so length = 18
6.The sum of 2 consecutive whole numbers is 105. Find the numbers.
Answer: 52, 53
- n + (n + 1) = 105
- 2n + 1 = 105
- n = 52
7.A rectangle is 5 cm longer than it is wide. Its perimeter is 90 cm. Find its width and length.
Answer: width 20 cm, length 25 cm
- 2(w + w + 5) = 90
- 4w + 10 = 90
- w = 20, so length = 25
8.A rectangle is 1 cm longer than it is wide. Its perimeter is 18 cm. Find its width and length.
Answer: width 4 cm, length 5 cm
- 2(w + w + 1) = 18
- 4w + 2 = 18
- w = 4, so length = 5
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.