Question

Emily Elizabeth has $1.50 in dimes and nickels. She has 22 coins in all. How many nickels does she have?

Answer 1

`14`

Explanation:

We can set up the following system of equations:

`\begin{cases}10d+5n=150\\d+n=22\\\end{cases}`, where
`d` is the number of dimes she has and
`n` is the number of nickels she has.

Multiplying the second equation by -5 and adding both equations lets us isolate and solve for
`d`:

`10d+5n+(-5(d+n))=150+(-5(22)),\\5d=40,\\d=8`

Plugging
`d=8` into any of the two equations will let us solve for
`n`:

`8+n=22,\\n=\fbox{$14$}`.

Therefore, she has 14 nickels.