Question

Jocelyn has $1.95 in her pocket made up of 27 nickels and dimes. How many of each type of coin does she have?

Answer 1

Jocelyn has 15 nickels and 12 dimes in her pocket.

Explanation:

First, let's call the number of dimes Jocelyn has `d` and the number of nickels she has `n`. We then know the number of dimes and the number of nickels are 27 or `d + n = 27`

We can solve this for `d`:

`d + n - n = 27 - n`

`d = 27 - n`

Next we know a dime is worth `$0.10` and a nickel is worth `$0.05` and we know she has a total of `$1.95` in her pocket so we can write:

`$0.10d + $0.05n = $1.95`

From the first equation we can substitute `27 - n` for `d` in the second equation and solve for `n`;

`$0.10(27 - n) + $0.05n = $1.95`

`($0.10*27) - $0.10n + $0.05n = $1.95`

`$2.70 - $0.05n = $1.95`

`$2.70 - $2.70 - $0.05n = $1.95 - $2.70`

`-$0.05n = -$0.75`

`(-$0.05n)/(-$0.05) = (-$0.75)/(-$0.05)`

`n = 15`

Now that we know there are 15 nickels (`n = 15`) we can substitute `15` for `n` in the solution for the first equation and calculate the number of dimes or `d`:

`d = 27 - 15`

`d = 12`