Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 A number is doubled and then 7 is added, giving 31. Which of these is the number?
Show worked solution
2 × 12 = 24, and 24 + 7 = 31, so the number is 12.
2 A number is multiplied by 4 and then 6 is subtracted, giving 30. Write the value after adding the 6 back, and the original number.
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30 + 6 = 36, then 36 ÷ 4 = 9.
3 A number is tripled and then 2 is added, giving 23. What is the number?
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23 − 2 = 21, and 21 ÷ 3 = 7.
Level 2 · Core
4 You are testing options for "5 times a number, plus 3, gives 38". You try 9 and get 48, which is too big. Which other option can you rule out straight away?
Show worked solution
Since bigger inputs give bigger outputs, anything above 9 also overshoots, so you can rule out the larger options. (The answer is 7.)
5 A number has 4 added, and the result is multiplied by 5, giving 45. Write the value after undoing the multiplication, and the original number.
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45 ÷ 5 = 9, then 9 − 4 = 5.
6 A number is halved and then 3 is added, giving 13. What is the number?
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13 − 3 = 10, and 10 × 2 = 20.
Level 3 · Challenge
7 Someone solves "a number times 4, minus 6, gives 30" by taking 30, dividing by 4, then adding 6.1 Their method reverses the operations but not the order.
2 Their method gives 13.5, which is wrong.
3 The correct answer is 9.
Which statements are correct?
2 Their method gives 13.5, which is wrong.
3 The correct answer is 9.
Which statements are correct?
Show worked solution
They flipped each operation but kept the original order (1 ✓). Their method gives 30 ÷ 4 = 7.5, then + 6 = 13.5 (2 ✓). Undoing properly gives 30 + 6 = 36, then ÷ 4 = 9 (3 ✓). 1, 2 and 3.
8 A number is doubled, then 5 is subtracted, then the result is tripled, giving 39. Write the value before the tripling, and the original number.
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39 ÷ 3 = 13, then 13 + 5 = 18, and 18 ÷ 2 = 9.
9 A number has 7 added, the result is doubled, and then 4 is taken away, giving 26. What was the number?
Show worked solution
26 + 4 = 30, then 30 ÷ 2 = 15, then 15 − 7 = 8.