Question

Georgia has only dimes and quarters in her bag. She has a total of 18 coins that are worth $3. How many more dimes than quarters does she have?

Answer 1

`2` more dimes than quarters.

Explanation:

In order to solve this, you need a system of equations (you need `2` separate equations with the same two variables and find out what values make them both true).

To start, you can say, since there are `18` coins and they are only dimes and quarters `d+q=18`.

Next, since dimes are worth `10¢`, quarters are worth `25¢`, and the total amount of cash is `300¢` you can say `10d+25q=300`.

Now you have `d+q=18` and `10d+25q=300`. There are several ways to solve a system of equations like this one. My personal preference is elimination as that is typically fastest.

Multiply everything in the first equation by `-10` so we can cancel our `d` and solve for `q`.
`d+q=18 rArr -10d-10q=-180`

Then, add the second equation to the one we just made.
`-10d-10q=-180`
`+10d+25q=300`

`-10d` and `10d` cancel and we are left with
`15q=120`

Divide both sides by 15.
`q=8`

Now, go back to your first equation and plug in your `q` value.
`d+8=18`

Subtract `8` from both sides
`d=10`

The original question wants to know how many more dimes you have than quarters. (`d-q=?`)
`10-8=2`