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?
Accepted Solution
A:
If x = # of quarters, then, the # of dimes will be equal to 2x. The total value (z) would be equal to: z = 0.25x + 0.10(2x) Then, since you switch the quarters and the dimes, and you have a new total, the resulting equation will be: 1.2 + z Β = 0.25(2x) + 0.10(x) Plug in the values you know: 1.2 + (0.25x + 0.10(2x)) = 0.25(2x) + 0.10(x) Solve for x: 1.2 + (0.25x + 0.20x) = 0.50x + 0.10x1.2 + 0.45x = 0.60x1.2 = 0.15xx = 1.2/0.15 = 8 This means that there are 8 Quarters in her bag right now. So, the amount of dimes is just 2x which is 16. So your answer will be: She has 8 Quarters and 16 Dimes in her bag right now. Or, $3.60. If this doesn't make sense, then tell me.