Question

The ratio of the number of chocolates Alice had to what Betty had was 7:8 at first. After Alice took 8 pieces and Betty took 4 pieces, the ratio became 4:5. What was the number of chocolates they had at first?

Answer 1

56 and 64

Explanation:

The initial ratio = 7 : 8 = 7x : 8x

After they have taken chocolates the ratio = 7x - 8 : 8x - 4 = 4 : 5

Expressing the ratios as equivalent fractions

`(7x-8)/(8x-4)` =
`(4)/(5)` ( cross- multiply )

5(7x - 8) = 4(8x - 4) ← distribute both sides

35x - 40 = 32x - 16 ( subtract 32x from both sides )

3x - 40 = - 16 ( add 40 to both sides )

3x = 24 ( divide both sides by 3 )

x = 8

Alice had 7x = 7 × 8 = 56

Betty had 8x = 8 × 8 = 64

Initially Alice had 56 chocolates and Betty had 64