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:
[tex]\begin{gathered} 0.25x+0.05y=15.40 \\ x+y=76 \end{gathered}[/tex]So, solve the system:
[tex]\begin{gathered} x+y-y=76-y \\ x=76-y \end{gathered}[/tex]Substitute x in the first equation:
[tex]0.25(76-y)+0.05y=15.40[/tex]Solve for y:
[tex]\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 \\ \frac{-0.20y}{-0.20}=\frac{-3.6}{-0.20} \\ y=18 \end{gathered}[/tex]Next, substitute y in x:
[tex]x=76-18=58[/tex]Answer: 58 quarters
18 nickles
