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 7 cm longer than it is wide. Its perimeter is 54 cm. Find its width and length.
Answer: width 10 cm, length 17 cm
- 2(w + w + 7) = 54
- 4w + 14 = 54
- w = 10, so length = 17
2.A rectangle is 9 cm longer than it is wide. Its perimeter is 78 cm. Find its width and length.
Answer: width 15 cm, length 24 cm
- 2(w + w + 9) = 78
- 4w + 18 = 78
- w = 15, so length = 24
3.Olivia buys some notebooks at $4.50 each and pays $8.00 for delivery. The total is $30.50. How many notebooks did Olivia buy?
Answer: 5
- 4.50n + 8.00 = 30.50
- 4.50n = 22.50
- n = 5
4.A rectangle is 6 cm longer than it is wide. Its perimeter is 76 cm. Find its width and length.
Answer: width 16 cm, length 22 cm
- 2(w + w + 6) = 76
- 4w + 12 = 76
- w = 16, so length = 22
5.Aisha buys some notebooks at $3.00 each and pays $4.00 for delivery. The total is $19.00. How many notebooks did Aisha buy?
Answer: 5
- 3.00n + 4.00 = 19.00
- 3.00n = 15.00
- n = 5
6.A rectangle is 2 cm longer than it is wide. Its perimeter is 68 cm. Find its width and length.
Answer: width 16 cm, length 18 cm
- 2(w + w + 2) = 68
- 4w + 4 = 68
- w = 16, so length = 18
7.A rectangle is 3 cm longer than it is wide. Its perimeter is 58 cm. Find its width and length.
Answer: width 13 cm, length 16 cm
- 2(w + w + 3) = 58
- 4w + 6 = 58
- w = 13, so length = 16
8.A rectangle is 10 cm longer than it is wide. Its perimeter is 56 cm. Find its width and length.
Answer: width 9 cm, length 19 cm
- 2(w + w + 10) = 56
- 4w + 20 = 56
- w = 9, 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.