Question 168128
{{{n}}}= number of nickels he has
{{{d}}}= number of dimes he has
Given is
(1) {{{n + d = 50}}}
(2) {{{d = 50 - n}}}
{{{.05n + .1d = 4.15}}}
Multiply both sides by {{{100}}}
(3) {{{5n + 10d = 415}}}
Substitute {{{d}}} in (2) for {{{d}}} in (3)
{{{5n + 10*(50 - n) = 415}}}
{{{5n + 500 - 10n = 415}}}
{{{-5n = -85}}}
{{{n = 17}}}
(2) {{{d = 50 - n}}}
{{{d = 50 - 17}}}
{{{d = 33}}}
He has 33 dimes and 17 nickels
check:
{{{.05n + .1d = 4.15}}}
{{{.05*17 + .1*33 = 4.15}}}
{{{.85 + 3.3 = 4.15}}}
{{{4.15 = 4.15}}}
OK