Your piggy bank has 25 coins in it; some are quarters and some are nickels. You have $3.45. How many nickels do you have?

First, let's call the number of quarters you have: `q`

And, the number of nickels you have: `n`

Using these variables and the information in the problem we can write two equations:

• Equation 1: `q + n = 25`

• Equation 2: `$0.25q + $0.05n = $3.45`

Step 1) Solve the first equation for `q`:

`q + n = 25`

`q + n - color(red)(n) = 25 - color(red)(n)`

`q + 0 = 25 - n`

`q = 25 - n`

Step 2) Substitute `(25 - n)` for `q` in the second equation and solve for `n` to find the number of nickels you have:

`$0.25q + $0.05n = $3.45` becomes:

`$0.25(25 - n) + $0.05n = $3.45`

`($0.25 xx 25) - ($0.25 xx n) + 0.05n = $3.45`

`$6.25 - $0.25n + 0.05n = $3.45`

`$6.25 + (-$0.25 + 0.05)n = $3.45`

`$6.25 + (-$0.20)n = $3.45`

`$6.25 - $0.20n = $3.45`

`$6.25 - color(red)($6.25) - $0.20n = $3.45 - color(red)($6.25)`

`0 - $0.20n = -$2.80`

`-$0.20n = -$2.80`

`(-$0.20n)/(color(red)(-)color(red)($)color(red)(0.20)) = (-$2.80)/(color(red)(-)color(red)($)color(red)(0.20))`

`(color(red)(cancel(color(black)(-$0.20)))n)/cancel(color(red)(-)color(red)($)color(red)(0.20)) = (color(red)(cancel(color(black)(-$)))2.80)/(cancel(color(red)(-)color(red)($))color(red)(0.20))`

`n = 2.80/color(red)(0.20)`

`n = 14`

You would have 14 nickels