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Forming & solving equations practice questions with answers

Foundation and Higher · Grade 4 · Non-calculator

A second set of forming & solving equations questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Sam and Tia have 20 sweets altogether. Tia has 4 times as many sweets as Sam. How many sweets does Sam have?

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Answer: 4

  1. Let Sam have n sweets. Then Tia has 4n.
  2. n + 4n = 5n = 20.
  • Method (1): Let Sam have n sweets. Then Tia has 4n.
  • Accuracy (1): Answer 4

Question 2 Easy

A rectangle has width n cm and length (n + 3) cm. Its perimeter is 42 cm. What is the length of the rectangle?

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Answer: 12

  1. Perimeter: 2n + 2(n + 3) = 42, so 4n + 6 = 42.
  2. 4n = 42 − 6 = 36, so n = 9.
  • Method (1): Perimeter: 2n + 2(n + 3) = 42, so 4n + 6 = 42.
  • Accuracy (1): Answer 12

Question 3 Medium

Sam and Tia have 18 sweets altogether. Tia has 5 times as many sweets as Sam. How many sweets does Sam have?

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Answer: 3

  1. Let Sam have n sweets. Then Tia has 5n.
  2. n + 5n = 6n = 18.
  • Method (1): Let Sam have n sweets. Then Tia has 5n.
  • Accuracy (1): Answer 3

Question 4 Medium

A rectangle has width n cm and length (n + 2) cm. Its perimeter is 28 cm. What is the length of the rectangle?

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Answer: 8

  1. Perimeter: 2n + 2(n + 2) = 28, so 4n + 4 = 28.
  2. 4n = 28 − 4 = 24, so n = 6.
  • Method (1): Perimeter: 2n + 2(n + 2) = 28, so 4n + 4 = 28.
  • Accuracy (1): Answer 8

Question 5 Hard

Sam and Tia have 33 sweets altogether. Tia has 2 times as many sweets as Sam. How many sweets does Sam have?

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Answer: 11

  1. Let Sam have n sweets. Then Tia has 2n.
  2. n + 2n = 3n = 33.
  • Method (1): Let Sam have n sweets. Then Tia has 2n.
  • Accuracy (1): Answer 11

Question 6 Hard

A rectangle has width n cm and length (n + 6) cm. Its perimeter is 24 cm. What is the length of the rectangle?

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Answer: 9

  1. Perimeter: 2n + 2(n + 6) = 24, so 4n + 12 = 24.
  2. 4n = 24 − 12 = 12, so n = 3.
  • Method (1): Perimeter: 2n + 2(n + 6) = 24, so 4n + 12 = 24.
  • Accuracy (1): Answer 9

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

A number is doubled and then 4 is added. The result is 14. What is the number?

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Answer: 5

  1. Let the number be n. Then 2n + 4 = 14.
  2. 2n = 14 − 4 = 10.
  3. n = 10 ÷ 2 = 5.
  • Method (1): Let the number be n. Then 2n + 4 = 14.
  • Accuracy (1): Answer 5

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

A number is trebled and then 3 is subtracted. The result is 21. What is the number?

  1. 8
  2. 24
  3. 6
Show answer

8 The result is 8.

Check 2

Sam and Tia have 45 sweets altogether. Tia has 4 times as many sweets as Sam. How many sweets does Sam have?

  1. 9
  2. 36
  3. 11.25
Show answer

9 The result is 9.

Check 3

A rectangle has width n cm and length (n + 4) cm. Its perimeter is 24 cm. What is the length of the rectangle?

  1. 8
  2. 4
  3. 6
Show answer

8 The result is 8.

Check 4

4 times a number, plus 5, is equal to the number plus 23. What is the number?

  1. 6
  2. 4.5
  3. 9.33
Show answer

6 The result is 6.

Check 5

A number is multiplied by 4 and then 7 is added. The result is 15. What is the number?

  1. 2
  2. 8
  3. 5.5
Show answer

2 The result is 2.

Check 6

Sam and Tia have 48 sweets altogether. Tia has 5 times as many sweets as Sam. How many sweets does Sam have?

  1. 8
  2. 40
  3. 9.6
Show answer

8 The result is 8.

Check 7

A rectangle has width n cm and length (n + 3) cm. Its perimeter is 38 cm. What is the length of the rectangle?

  1. 11
  2. 8
  3. 9.5
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11 The result is 11.

Check 8

2 times a number, plus 4, is equal to the number plus 11. What is the number?

  1. 7
  2. 3.5
  3. 15
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7 The result is 7.

Check 9

A number is multiplied by 5 and then 6 is subtracted. The result is 19. What is the number?

  1. 5
  2. 25
  3. 2.6
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5 The result is 5.

Check 10

Sam and Tia have 21 sweets altogether. Tia has 2 times as many sweets as Sam. How many sweets does Sam have?

  1. 7
  2. 14
  3. 10.5
Show answer

7 The result is 7.

Check 11

A rectangle has width n cm and length (n + 2) cm. Its perimeter is 24 cm. What is the length of the rectangle?

  1. 7
  2. 5
  3. 6
Show answer

7 The result is 7.

Check 12

3 times a number, plus 3, is equal to the number plus 19. What is the number?

  1. 8
  2. 5.33
  3. 11
Show answer

8 The result is 8.

Check 13

A number is doubled and then 5 is added. The result is 21. What is the number?

  1. 8
  2. 16
  3. 13
Show answer

8 The result is 8.

Check 14

Sam and Tia have 24 sweets altogether. Tia has 3 times as many sweets as Sam. How many sweets does Sam have?

  1. 6
  2. 18
  3. 8
Show answer

6 The result is 6.

Check 15

A rectangle has width n cm and length (n + 6) cm. Its perimeter is 48 cm. What is the length of the rectangle?

  1. 15
  2. 9
  3. 12
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15 The result is 15.

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