Jenny has 6 quarters and some nickels. The total value of her coins is $3.15. How do you write and solve an equation for this?

`6 xx 25` equals the value of the quarters

`x xx 5` equals the value of the nickels

315 equals the value of the total of quarters and nickels.

`6 xx 25 + x xx 5 = 315` multiply to find the value of quarters.

`150 + 5x = 315` subtract 150 from both sides

`150 - 150 + 5x = 315 -150`

`5x = 165` divide both sides by 5

`(5x)/5 = 165/5`

`x = 33`

There are 33 nickels

A quarter is $0.25, let's call that value q.

`6q = $1.5`

A nickel is $0.05, and we have an unknown n amount of them.

`"Final equation: " $1.5 + (n * $0.05) = $3.15`

Now we solve the equation, substracting `$1.5` on both sides:

`(n * $0.05) = $1.65`

Dividing both sides by `$0.05`:

`n = 33`

We can write and equation for this problem as:

`t = $0.25q + $0.05n`

Where:

`t` is the total value of the coins, $3.15 for this problem.

`q` is the number of quarters multiplied by their value of $0.25. This is `6` for this problem.

`n` is the number of nickels multiplied by the value of $0.05. This is what we are solving for in this problem.

Substituting what we know and solving for `n` gives:

`$3.15 = ($0.25 * 6) + $0.05n`

`$3.15 = $1.50 + $0.05n`

`$3.15 - color(red)($1.50) = -color(red)($1.50) + $1.50 + $0.05n`

`$1.65 = 0 + $0.05n`

`$1.65 = $0.05n`

`($1.65)/color(red)($0.05) = ($0.05n)/color(red)($0.05)`

`(color(red)(cancel(color(black)($)))1.65)/color(red)(color(black)(cancel(color(red)($)))0.05) = (color(red)(cancel(color(black)($0.05)))n)/cancel(color(red)($0.05))`

`1.65/color(red)(0.05) = n`

`33 = n`

`n = 33`

Jenny has `color(red)(33)` nickels along with her `6` quarters