Debbi has 17 coins that are all either quarters or dimes. the total value of her money is 3.20

There are 10 quarters and 7 dimes

Step-by-step explanation:

The question asks for the number of quarters and the number of dimes.

Quarters and Dimes equal 17, so let number of quarters be "q" and number of dimes be "d", so we can write:

q + d = 17

We know quarters are worth 0.25 and dimes are worth 0.10 (in dollars) and total value of the coins are 3.20 dollars, thus we can write:

0.25q + 0.10d = 3.20

Let's write the first equation as:

q = 17 - d

Now we substitute this into 2nd equation and solve for d:

0.25q + 0.10d = 3.20

0.25 (17 - d) + 0.10d = 3.20

4.25-0.25d+0.10d = 3.20

-0.15d = - 1.05

d = 7

Now using this value of d, we now find q:

q = 17 - d

q = 17 - 7

q = 10

There are 10 quarters and 7 dimes