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 Two stars are worth 14. A star and a heart are worth 10. What is a heart worth?
Show worked solution
A star is 14 ÷ 2 = 7, so a heart is 10 − 7 = 3.
2 □ + △ = 15 and □ − △ = 3. Find □ and △.
Show worked solution
□ = 9 and △ = 6: 9 + 6 = 15 and 9 − 6 = 3.
3 Three hearts are worth 21. What is one heart plus 5?
Show worked solution
A heart is 7, so 7 + 5 = 12.
Level 2 · Core
4 A + B = 20, B + C = 26, A + C = 30. What is B?
Show worked solution
Total = 76 ÷ 2 = 38. B = 38 − (A + C) = 38 − 30 = 8.
5 2 apples and 1 pear cost $7. 2 apples and 3 pears cost $13. Find the cost of a pear and of an apple, in dollars.
Show worked solution
2 pears = $6, so a pear is $3. Then 2 apples + 3 = 7, so an apple is $2.
6 ★ = ♥ + 4 and ★ + ♥ = 20. What is ★?
Show worked solution
♥ + 4 + ♥ = 20, so ♥ = 8 and ★ = 12.
Level 3 · Challenge
7 A team won 16 medals and 36 points (gold 3, silver 2, bronze 1). 6 medals were silver.1 Gold and bronze medals together number 10.
2 They won 7 gold medals.
3 They won 4 bronze medals.
Which statements are correct?
2 They won 7 gold medals.
3 They won 4 bronze medals.
Which statements are correct?
Show worked solution
16 − 6 = 10 gold and bronze (1 ✓), worth 36 − 12 = 24. 7 gold + 3 bronze = 21 + 3 = 24 (2 ✓, 3 ✗). 1 and 2.
8 Three boxes weighed in pairs: 28 kg, 32 kg and 38 kg. Give the total mass of all three, and the mass of the heaviest box.
Show worked solution
Total = 98 ÷ 2 = 49. Boxes: 49 − 32 = 17, 49 − 38 = 11, 49 − 28 = 21.
9 4 stars and 2 hearts are worth 26. A star and a heart together are worth 8. What is a star worth?
Show worked solution
4 stars + 2 hearts = 26 and 2 stars + 2 hearts = 16, so 2 stars = 10 and a star is 5.