Pete used $$\frac{5}{6}$$ for the cupboard, so $$\frac{1}{6}$$ remained. He used $$\frac{1}{4}$$ of the remainder for the shoe-rack.<br><br>[[model:questions/solutions/q4346.png]]<br><br>• Cupboard → $$\frac{5}{6}$$ of whole = $$\frac{20}{24}$$<br>• Remainder → 1 − $$\frac{5}{6}$$ = $$\frac{1}{6}$$ = $$\frac{4}{24}$$<br>• Shoe-rack → $$\frac{1}{4}$$ × $$\frac{4}{24}$$ = $$\frac{1}{24}$$ → 1u<br>• Left → 4u − 1u = 3u → 36 nails<br>• 1u → 36 ÷ 3 = 12 ⇒ whole 24u → 24 × 12 = 288<br><br>Pete had 288 nails at first.<br>Check: Cupboard = $$\frac{5}{6}$$ × 288 = 240. Remaining = 48. Rack = $$\frac{1}{4}$$ × 48 = 12. Left = 36. ✓