Question

A person has a total of 65 coins in a jar consisting of quarters and nickles. The total value of the coins is $10.25. How many quarters and nickles does the person have?

Answer 1

See a solution process below:

Explanation:

First:

Let's call the number of quarters: `q`

Let's call the number of nickles: `n`

We know:

`q + n = 65` because there are 65 coins in the jar.

We also know multiplying the value of the coins by the number of coins gives: `0.25q + 0.05n = $10.25`

Step 1) We can now solve the first equation for `q`:

`q + n = 65`

`q + n - color(red)(n) = 65 - color(red)(n)`

`q + 0 = 65 - n`

`q = 65 - n`

Step 2) Substitute `(65 - n)` for `q` in the second equation and solve for `n`:

`0.25q + 0.05n = 10.25` becomes:

`0.25(65 - n) + 0.05n = 10.25`

`(0.25 * 65) - (0.25 * n) + 0.05n = 10.25`

`16.25 - 0.25n + 0.05n = 10.25`

`16.25 + (-0.25 + 0.05)n = 10.25`

`16.25 + (-0.2)n = 10.25`

`16.25 - 0.2n = 10.25`

`-color(red)(16.25) + 16.25 - 0.2n = -color(red)(16.25) + 10.25`

`0 - 0.2n = -6`

`-0.2n = -6`

`(-0.2n)/color(red)(-0.2) = -6/color(red)(-0.2)`

`(color(red)(cancel(color(black)(-0.2)))n)/cancel(color(red)(-0.2)) = 30`

`n = 30`

Step 3) Substitute `30` for `n` in the solution to the first equation at the end of Step 1 and calculate `q`:

`q = 65 - n` becomes:

`q = 65 - 30`

`q = 35`

The solution is: `n = 30` and `q = 35`

So there are `30` nickles and `35` quarters.