The number of Quarters is 7. Here's how to find them. Let Q (H) be the number of Quarters (Half-dollars). The problem tells us that 0.25*Q + 0.50*H = 10.25. Now multiply both sides by 100 to simply the arithmetic, yielding

25Q + 50 H = 1025 and Q+H = 24, so that H = 24 - Q. Now plug in 24 -Q for H in the equation

25Q + 50 H = 1025. You'll get 25Q + 50(24-Q) = 1025. Now solve for Q.