n= each nickle = 0.05 dollars
d= each dime = 0.1 dollars
so
[tex]0.05n + 0.1d = 8.55[/tex]
and
[tex]n + d = 117[/tex]
[tex]d = 117 - n[/tex]
solving the 2 equations for the 2 variables:
[tex]0.05n + 0.1(117 - n) = 8.55[/tex]
[tex] - 0.05n = 8.55 - 11.7 = - 3.15[/tex]
[tex]n = \frac{ - 3.15}{ - 0.05} = 63 \: nickles[/tex]
[tex]n + d = 117[/tex]
[tex]d = 117 - 63 = 54 \: dimes[/tex]
