Answer:
$450
Step-by-step 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:
[tex]E:J:R = 5:6:9[/tex]
This means Ethan has 5/20 of M, the money to start with. This reduces to 1/4 of M.
Afterwards:
[tex](E-50):J:R = 3:4:6[/tex]
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
[tex](E - 50) = 3/13 * (M - 50)[/tex]
We know 4E = M, so we can substitute that in:
[tex](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[/tex]
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.
