Question

5. A sum of money is divided among Ethan, Jun Wei

and Raj in the ratio 5:6:9. After Ethan gives $50
Find the amount of money Ethan has after giving
to his mother, the ratio becomes 3:4:6.
$50 to his mother.
(Step by step explain pls)

Answer 1

$450

Explanation:

Let E be the amount of money Ethan starts with, J be the amount Jun Wei starts with, and R be the amount Raj starts with. Let M be the total amount of money to start with.

To start:

`E:J:R = 5:6:9`

This means Ethan has 5/20 of M, the money to start with. This reduces to 1/4 of M.

Afterwards:

`(E-50):J:R = 3:4:6`

This means Ethan has 3/13 of the remaining money (which is M-50!) after giving up 50. So

E = (M/4), or 4E = M

and

`(E - 50) = 3/13 * (M - 50)`

We know 4E = M, so we can substitute that in:

`(E - 50) = 3/13 * (4E - 50)E - 50 = (12/13)E - 150/13E - 650/13 = (12/13)E - 150/13(1/13)E = 500/13E = 500`

That's how much money Ethan had to start with. But we're asked how much he has AFTER giving $50 away, so that's $450.