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?
I need help with this t00
so, what have they told you?
d = 2q
10q+25d = 10d+25q + 120
now just find d and q
To solve this problem, we can set up a system of equations.
Let's assume that the woman has x quarters and 2x dimes in her purse currently.
The value of quarters in her purse is 25 cents each, so the total value of quarters is 25 * x cents.
The value of dimes in her purse is 10 cents each, so the total value of dimes is 10 * 2x = 20 * x cents.
According to the given information, if the dimes were quarters and the quarters were dimes, she would have $1.20 more than she currently has. We can express this relationship with the equation:
25 * (2x) + 10 * x = 20 * x + 1.20
Simplifying this equation, we get:
50x + 10x = 20x + 1.20
60x = 20x + 1.20
60x - 20x = 1.20
40x = 1.20
x = 1.20 / 40
x = 0.03
Now we know that she has 0.03 quarters and 2 * 0.03 = 0.06 dimes in her purse.
However, since we cannot have a fraction of a coin, we need to convert these values into whole numbers. Let's multiply everything by 100 to get rid of decimals:
0.03 * 100 = 3 quarters
0.06 * 100 = 6 dimes
So, the woman has 3 quarters and 6 dimes in her purse now.