I have a math problem that I solved, but I can't explain why

Question

The top three prizes in a golf tournament totaled $126,000. The golfer who finsihed second recieved twice as much as the golfer who finished third. The winner of the tournament recieved three times as much as the golfer who finsihed second. The winner recieved ___________.

I can solve that 1st got $84,000,  2nd got $28,000, and 3rd got $14,000 but I don't know why.

Answer 1

Let the 3rd golfer receive $ x.

So, 2nd golfer received  2x

And 3rd golfer received 3* amount of 2nd golfer = 3 * (2x) = 6x

Therefore,  x + 2x + 6x = 126000

or 9x = 126000 => x = 14000

So, 3rd golfer received = $14000

2nd golfer received = 2x = 2 * 14000 = $28000

1st golfer received = 6x = 6 * 14000 = $84000