Problem Solving

Hi there,

I don't know clearly diagram this PS in order to resolve it. Could you show me a fast way to understand and resolve it.

A certain scholarship committee awarded scholarships in the amounts of 1250$, 2500$, and 4000$. The committee awarded twice as many 2500 scholarships as 4000$ scholarships, and it awarded 3 times as many as 1250$ scholarships as 2500$. If a total of 37 500$ was awarded in 1250$, how many 4000$ scholarships were awarded ?

a) 5
b) 6
c) 9
d) 10
e) 15

oa is A

From the problem we can make following:
Let the number of 4000$ scholarship is x, then 2500 - 2x, and 1250 - 6x (three times greater than 2500)
now 6x*1250 = 37500
6x = 30
x = 5

A is the answer

many thks