Kat has 19 coins, all quarters and dimes, that are worth a total of $4. the system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown. q + d = 19 0.25q + 0.1d = 4

Since q+d=19, we can re-write this as d=19-q. Using the second equation 0.25q+0.1d=4 we can multiply both sides by 100. So we get 25q+10d=400. So now we can plug d=19-q into 25q+10d=400. So now we get, 25q+190-10q=400. Subtracting both sides by 190, we get 15q=210 and that q=14 plugging that in d=5