Dogs are $$\frac{1}{2}$$ of all animals, so $$\frac{1}{2}$$ remained. Cats are $$\frac{4}{5}$$ of the remainder, hamsters are the rest.<br><br>[[model:questions/solutions/q4348.png]]<br><br>• Dogs → $$\frac{1}{2}$$ of whole = $$\frac{5}{10}$$<br>• Remainder → 1 − $$\frac{1}{2}$$ = $$\frac{1}{2}$$ = $$\frac{5}{10}$$<br>• Cats → $$\frac{4}{5}$$ × $$\frac{5}{10}$$ = $$\frac{4}{10}$$ → 4u<br>• Hamsters → 5u − 4u = 1u<br>• Dogs − Cats → 5u − 4u = 1u → 10 animals ⇒ Hamsters = 1u = 10<br><br>Jamie has 10 hamsters.<br>Check: Total = 10 × 10 = 100. Dogs = 50. Cats = 40. Hamsters = 10. Dogs − Cats = 10. ✓