Question

Ashley has $9.05 in dimes and nickels. If she has a total of 108 coins, how many of each type does she have?

Answer 1

Answer:

$73\:\mathrm{dimes},\\35\:\mathrm{nickels}$

Step-by-step explanation:

We can write the following system of equations:

$\begin{cases}10d+5n=905,\\d+n=108,\\\end{cases}$, where $d$ is the number of dimes she has and $n$ is the number of nickels she has.

Multiply the second equation by $-5$ and add both equations to solve for $d$:

$\begin{cases}10d+5n=905,\\-5d-5n=-540,\\\end{cases}\\5d=365,\\d=\fbox{ 73 }$.

Plug $d=73$ into any equation to solve for $n$:

$73+n=108, \\n=\fbox{ 35 }$