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