Question

Julie collects dimes and quarters. She has a total of 98 dimes and quarters in a jar. She counted the money and found out she has $14.90 in the jar. How many dimes and quarters does she have?

Answer 1

64 dimes and 34 quarters.

Explanation:

Let d represent the amount of dimes and q represent the amount of quarter Julie has.

She has in total 98 coins. Therefore:

`d+q=98`

Each dime is worth 0.10 and each quarter is worth 0.25. Together, they are worth in total $14.90. Therefore:

`0.1d+0.25q=14.90`

We have a system of equations. We can solve this using substitution.

First, we can multiply the second equation by 100 to simplify. So:

`10d+25q=1490`

From the first equation, we can subtract q from both sides:

`d=98-q`

Substitute this into the second equation:

`10(98-q)+25q=1490`

Distribute:

`980-10q+25q=1490`

Combine like term:

`15q+980=1490`

Subtract:

`15q=510`

Therefore:

`q=34`

So, Julie has 34 quarters.

Returning to our first equation:

`d+q=98`

Substitute:

`d+34=98`

Therefore:

`d=64`

Thus, Julie has 64 dimes and 34 quarters.