Year 10 Equation Word Problems Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 10 linear equations worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Linear EquationsYear 10 Equation Word Problems Worksheet — Level 2 — 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.Ethan thinks of a number, multiplies it by 3 and then adds 3. The answer is 15. Write an equation and find the number.
Answer: 4
- Let the number be n: 3n + 3 = 15
- 3n = 12
- n = 4
2.A rectangle is 3 cm longer than it is wide. Its perimeter is 54 cm. Find its width and length.
Answer: width 12 cm, length 15 cm
- 2(w + w + 3) = 54
- 4w + 6 = 54
- w = 12, so length = 15
3.A rectangle is 10 cm longer than it is wide. Its perimeter is 64 cm. Find its width and length.
Answer: width 11 cm, length 21 cm
- 2(w + w + 10) = 64
- 4w + 20 = 64
- w = 11, so length = 21
4.Cooper thinks of a number, subtracts 8 and multiplies the result by 5. The answer is 75. What was the number?
Answer: 23
- 5(n − 8) = 75
- n − 8 = 15
- n = 23
5.Jack thinks of a number, multiplies it by 3 and then adds 3. The answer is 12. Write an equation and find the number.
Answer: 3
- Let the number be n: 3n + 3 = 12
- 3n = 9
- n = 3
6.The sum of 2 consecutive whole numbers is 15. Find the numbers.
Answer: 7, 8
- n + (n + 1) = 15
- 2n + 1 = 15
- n = 7
7.A rectangle is 6 cm longer than it is wide. Its perimeter is 40 cm. Find its width and length.
Answer: width 7 cm, length 13 cm
- 2(w + w + 6) = 40
- 4w + 12 = 40
- w = 7, so length = 13
8.The sum of 3 consecutive whole numbers is 72. Find the numbers.
Answer: 23, 24, 25
- n + (n + 1) + (n + 2) = 72
- 3n + 3 = 72
- n = 23
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.