A sum of money is divided among Khairul, Michael and Ethan in the ratio 6:4: 5. After Khairul gives $30 to Michael and $15 to Ethan, the ratio
becomes 7:6:7. Find the amount of money Khairul had initially.​

$360

Step-by-step explanation:

The intial ratio of the sum shared between Khairul, Michael and Ethan is 6 : 4 : 5.

This would be 6x : 4x : 5x

Khairul gives $30 to Michael and $15.

The ratio is. Now;

(6x - 45) : (4x + 30) : (5x + 15)

We are told this is equal to the ratio 7:6:7

Thus;

((6x - 45) + (4x + 30))/(5x + 15) = (7 + 6)/7

(10x - 15)/(5x + 15) = 13/7

Factorize the left hand side;

5(2x - 3)/5(x + 3) = 13/7

5 will cancel out to get;

(2x - 3)/(x + 3) = 13/7

Cross multiply to get;

7(2x - 3) = 13(x + 3)

14x - 21 = 13x + 39

14x - 13x = 39 + 21

x = 60

Amount Khairul had initially was denoted as 6x.

Thus,6x = 5 × 60 = $360