Showing a scale factor of 3/2

let x be number of half-dollars and y be number of dimes

total value: 0.5x + 0.1y = 3.60

total amount: x + y = 24

solving this system of equations, we get that x = 3 and y = 21. (a proof of this fact has been left to the reader.) so there are 3 half dollars and 21 dimes.