Question

James has 33 coins in his pocket, all of them nickels and quarters. If he has a total of $2.25, how many quarters does he have?

Answer 1

James has `"3 quarters"`

Explanation:

I'm going to give nickels and quarters their own variable. Nickels will be `n` and quarters will be `q`. Since he has `"33 total"` we can write this equation:
`n + q = 33`

The second part is about the `"value"` of the nickels and quarters. Since nickels are worth `"5 cents"` and quarters are worth `"25 cents"` we can make this equation:

`0.05n + 0.25q = 2.25`

I'm actually going to multiply this whole equation by `100` to move the decimal point 2 places and make it easier to solve:

`5n + 25q = 225`

We need to find how many `"quarters"` he has, so we need to leave `q` in the equation so that we can solve for it. So let's rearrange the first equation:
`n + q = 33 rarr n = 33 - q`

Now substitute it into the second equation:
`5n + 25q = 225`

`5(33 - q) + 25q = 225`
`165 - 5q + 25q = 225`
`165 + 20q = 225`
`20q = 60`
`q = 3`