A pet shop kept rabbits in Cage X and Cage Y. Cage X had four times as many rabbits as Cage Y. In Cage X, 38 of the rabbits were white. In Cage Y, 23 of the rabbits were white. What fraction of all the rabbits were white? Give your answer in simplest form.
Need a hint?
Work out the rabbits in each cage using the 4 : 1 ratio first, then find how many white rabbits there are in each cage before comparing with the total.
Worked answer
- Let Cage Y have 1 unit of rabbits, so Cage X has 4 units and the total is 5 units.
- White rabbits in Cage X: 38 of 4 units = 32 units.
- White rabbits in Cage Y: 23 of 1 unit = 23 units.
- Total white rabbits: 32 + 23 = 136 units.
- Fraction white: 136 ÷ 5 = 1330. (Check: Cage Y 24 rabbits, Cage X 96; white 16 + 36 = 52 out of 120, which is 1330.)
The mistake this question tests
Stopped at one part in ratio
Averaging the two fractions, (38 + 23) ÷ 2, ignores that Cage X holds four times as many rabbits as Cage Y, so the cages must be weighted by their sizes.
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