Dogs are $$\frac{1}{3}$$ of all animals, so $$\frac{2}{3}$$ remained. Cats are $$\frac{1}{6}$$ of the remainder, hamsters are the rest.<br><br>[[model:questions/solutions/q4349.png]]<br><br>• Dogs → $$\frac{1}{3}$$ of whole = $$\frac{6}{18}$$<br>• Remainder → 1 − $$\frac{1}{3}$$ = $$\frac{2}{3}$$ = $$\frac{12}{18}$$<br>• Cats → $$\frac{1}{6}$$ × $$\frac{12}{18}$$ = $$\frac{2}{18}$$ → 2u<br>• Hamsters → 12u − 2u = 10u<br>• Dogs − Cats → 6u − 2u = 4u → 12 animals ⇒ 1u = 3 ⇒ Total = 18 × 3 = 54<br><br>There are 54 animals in the shop.<br>Check: Dogs = 6 × 3 = 18. Cats = 2 × 3 = 6. 18 − 6 = 12. ✓