How many quarters and dimes?

Question

A collection of dimes and quarters is worth $9.55. If the quarters were dimes and the dimes were quarters, the total value would be $7.60. Find the number of each coin. 

Answer 1

q represents the number of quarter

d repersents the number of dimes

0.25q + 0.10d = 9.55

0.10q + 0.25d = 7.60 switch number of each

0.25q + 0.10d = 9.55

0.25q + 0.625d = 19.00 multiplied by 2.5

0.525d = 9.45 subtract top from bottom

d = 18

How many quarters?