A woman has twice as many dimes as quarters in her purse. If the dimes were quarters and the quarters were dimes, she would have $1.20 more than she now has. How many of each does she have now?

Let x = number of quarters since she has twice as many dimes as quarters, Let 2x = number of dimes The total value in $ is 0.25x + (0.10)(2x) And it was said that when the numbers of quarters and dimes are interchanged, she would have $1.20 more than the original. So, (New Value) = (Original Value) + $1.20 0.25(2x) + 0.10x = 0.25x + (0.10)(2x) + 1.20 Solving for x, 0.5x + 0.1x = 0.25x + 0.2x + 1.20 0.6x = 0.45x + 1.20 0.6x - 0.45x = 1.20 0.15x = 1.20 x = 1.20/0.15 x = 8 quarters 2x = 16 dimes