I can see two ways to approach this problem. The first is using algebra.
Let x be the number of 0.10$ pieces then, since there are 250 coins in total, there are 250 - x coins with a value of 0.25$. The total value of the x, 0.10$ pieces is x 0.10$. The total value of the x, 0.25$ pieces is (250 - x) 0.25$. But in total the value is 36.75$ and hence
x 0.10$ + (250 - x) 0.25$ = 36.75$
Solve for x.
The Second technique doesn't use algebra.
Suppose that all 250 coins are 0.25$ coins then the value is 250 0.25$ = 62.50$. But the sum is to be 36.25$ so 62.50$ is 62.50$ - 36.25$ = 26.25$ too much. If you replace one 0.25$ coin by a 0.10$ coin you reduce the total by 0.15$. How many reductions of 0.15$ are needed to reduce the sum from 62.50$ to 36.25$?
Whichever technique you use you should check your answer.