AQA · Mathematics · 8300

GCSE Maths: Equations: Think of a number

Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Equations: Think of a number (Corbettmaths Video 116), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.

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  1. Ava multiplies a number by 3, then adds 9 to get 45. What was her starting number?

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    12. Working backwards: (45 − 9) ÷ 3 = 36 ÷ 3 = 12.

  2. Jack multiplies a number by 4 and then adds 5 to get 33. What number is he thinking of?

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    7. Working backwards: (33 − 5) ÷ 4 = 28 ÷ 4 = 7.

  3. Danielle subtracts 11 from a number, then multiplies by 7 to get 77. What number is she thinking of?

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    22. Working backwards: 77 ÷ 7 = 11, then 11 + 11 = 22.

  4. Lauren divides a number by 8, then multiplies by 5 to get 45. What number is she thinking of?

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    72. Working backwards: 45 ÷ 5 = 9, then 9 × 8 = 72.

  5. Harry divides a number by 4, subtracts 1, then multiplies by 6 to get 72. What was his starting number?

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    52. Working backwards: 72 ÷ 6 = 12, then 12 + 1 = 13, then 13 × 4 = 52.

  6. Jemimah squares a positive number and then subtracts 4 to get 60. What was her number?

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    8. Working backwards: 60 + 4 = 64, then √64 = 8.

  7. Leo finds the square root of a number and then adds 10 to get 35. What number is he thinking of?

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    625. Working backwards: 35 − 10 = 25, then 25² = 625.

  8. Joanne multiplies a number by 2, then adds 10 to get 4. What was her starting number?

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    −3. Working backwards: (4 − 10) ÷ 2 = −6 ÷ 2 = −3.

  9. Adele multiplies a number by 6 and then subtracts 80. Her answer equals the number she started with. What was the number?

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    16. Solving 6x − 80 = x gives 5x = 80, so x = 16.

  10. Reece adds a third of a number to a quarter of the number to get 35. What was the number?

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    60. Solving (1/3)x + (1/4)x = 35 gives (7/12)x = 35, so x = 60.

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