Question

I have $15.40 in quarters and nickels. I have 76 coins altogether. How many quarters? How many nickels?

Answer 1

We have:

Let x = the number of quarters

Let y = the number of nickels

And

Quarter = $0.25

Nickel = $0.05

Then, we have the following expressions:

`\begin{gathered} 0.25x+0.05y=15.40 \\ x+y=76 \end{gathered}`

So, solve the system:

`\begin{gathered} x+y-y=76-y \\ x=76-y \end{gathered}`

Substitute x in the first equation:

`0.25(76-y)+0.05y=15.40`

Solve for y:

`\begin{gathered} 19-0.25y+0.05y=15.40 \\ 19-0.20y=15.40 \\ 19-0.20y-19=15.40-19 \\ -0.20y=-3.6 \\ (-0.20y)/(-0.20)=(-3.6)/(-0.20) \\ y=18 \end{gathered}`

Next, substitute y in x:

`x=76-18=58`

Answer: 58 quarters

18 nickles