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

Question

rjkz [21]

3 years ago

10

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?

Mathematics

2 answers:

Fudgin [204] · Answer 1 · 2022-03-02T18:12:42+03:00

Fudgin [204]3 years ago

6 0

Answer:

8 Quarters and 16 Dimes

Digiron [165] · Answer 2 · 2022-03-02T16:50:34+03:00

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 = 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 + 0.10x
1.2 + 0.45x = 0.60x
1.2 = 0.15x
x = 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. I have some resources where I got the answer from to put it into simplest terms. I have the website if you want.