Question

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

Answer 1

Answer:

$14$

Step-by-step 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.