Question

The ratio of yellow sweets to purple sweets is 5:4.

Alice eats 3 purple sweets and the ratio is now 5:3.

Work out how many sweets there were at the beginning.

Answer 1

27

Explanation:

The ratio of yellow : purple = 5 : 4 = 5x : 4x ( x is a multiplier )

After Alice eats 3 purple sweets, then ratio is

5 : 3 = 5x : 4x - 3

Express the ratio in fractional form, that is

`(5)/(3)` =
`(5x)/(4x-3)` ( cross- multiply )

5(4x - 3) = 15x

20x - 15 = 15x ( subtract 15x from both sides )

5x - 15 = 0 ( add 15 to both sides )

5x = 15 ( divide both sides by 5 )

x = 3

Then

number of sweets at beginning = 5x + 4x = 9x = 9(3) = 27