Matt used $$\frac{4}{5}$$ for the cupboard, so $$\frac{1}{5}$$ remained. He used $$\frac{1}{5}$$ of the remainder for the shoe-rack.<br><br>[[model:questions/solutions/q4345.png]]<br><br>• Cupboard → $$\frac{4}{5}$$ of whole = $$\frac{20}{25}$$<br>• Remainder → 1 − $$\frac{4}{5}$$ = $$\frac{1}{5}$$ = $$\frac{5}{25}$$<br>• Shoe-rack → $$\frac{1}{5}$$ × $$\frac{5}{25}$$ = $$\frac{1}{25}$$ → 1u<br>• Left → 5u − 1u = 4u → 48 nails<br>• 1u → 48 ÷ 4 = 12 ⇒ Cupboard − Rack = 20u − 1u = 19u → 19 × 12 = 228<br><br>Matt used 228 more nails for the cupboard than for the shoe-rack.<br>Check: Total = 25 × 12 = 300. Cupboard = $$\frac{4}{5}$$ × 300 = 240. Remaining = 60. Rack = $$\frac{1}{5}$$ × 60 = 12. Left = 48. ✓