Question

Andy and bart have marbles in the ratio 4:5. andy loses 9 and the ratio now is 5:7. how many did they each have initially ?​

Answer 1

Andy = 84 and Bart = 105

Explanation:

Given that the ratio is 4 : 5 = 4x : 5x

Andy loses 9 thus 4x - 9

ratio 4x - 9 : 5x = 5 : 7, that is

`(4x-9)/(5x)` =
`(5)/(7)` ( cross- multiply )

25x = 7(4x - 9) ← distribute

25x = 28x - 63 ( subtract 28x from both sides )

- 3x = - 63 ( divide both sides by 3 )

x = 21

Hence

Andy = 4x = 4 × 21 = 84 marbles

Bart = 5x = 5 × 21 = 105 marbles