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 has 8 added, then the result is doubled, giving 30. What was the number?
Show worked solution
30 ÷ 2 = 15, then 15 − 8 = 7. Check: 7 + 8 = 15, × 2 = 30 ✓.
2 A number is multiplied by 4, then 9 is added, giving 61. Give the number after undoing the + 9, then the starting number.
Show worked solution
61 − 9 = 52. 52 ÷ 4 = 13.
3 I think of a number, subtract 14, and get 29. What is my number?
Show worked solution
29 + 14 = 43.
Level 2 · Core
4 Ravi had some money. He spent half of it, then spent $3.50, and had $6.50 left. How much did he start with?
Show worked solution
6.50 + 3.50 = 10, and that is half, so he started with $20.
5 A number is halved three times and ends at 7. Give the number before the third halving, before the second, and at the start.
Show worked solution
7 × 2 = 14, × 2 = 28, × 2 = 56.
6 A number is tripled and then 11 is subtracted, giving 40. What was the number?
Show worked solution
40 + 11 = 51, then 51 ÷ 3 = 17.
Level 3 · Challenge
7 Zoe doubles a number, adds 6, then halves the result, and gets 11.1 Zoe's number is 8.
2 Whatever number Zoe starts with, the result is always 3 more than it.
3 Zoe's number is 16.
Which statements are correct?
2 Whatever number Zoe starts with, the result is always 3 more than it.
3 Zoe's number is 16.
Which statements are correct?
Show worked solution
11 × 2 = 22, 22 − 6 = 16, 16 ÷ 2 = 8 (1 ✓, 3 ✗ — 16 is the number after doubling). Doubling, adding 6 and halving gives start + 3 every time: 8 → 11 (2 ✓). 1 and 2.
8 Alan had $10. He gave some to Kiana, half of what was left to Jason, and Jason gave half of his to Lenny, who got $1.60. Give Jason's amount, Alan's amount after giving to Kiana, and Kiana's amount, in dollars.
Show worked solution
Jason: 2 × 1.60 = 3.20. Alan after Kiana: 2 × 3.20 = 6.40. Kiana: 10 − 6.40 = 3.60.
9 A number has 25 added, the result is halved, then 7 is subtracted, giving 20. What was the number?
Show worked solution
20 + 7 = 27, × 2 = 54, − 25 = 29. Forwards: 29 + 25 = 54, halved 27, − 7 = 20 ✓.