Question 180987
Let {{{n}}} = number of nickels
Let {{{d}}} = number of dimes
Let {{{q}}} = number of quarters
given:
(1) {{{d = q + 4}}}
(1) {{{q = d - 4}}}
(2) {{{n = 2d}}}
(3) {{{5n + 1d + 25q = 440}}} (in cents)
Substitute {{{d-4}}} in (1) and {{{2d}}} in (2) for 
{{{q}}} and {{{n}}} in (3)
(3) {{{5(2d) + 1d + 25(d - 4) = 440}}}
{{{10d + d + 25d - 100 = 440}}}
{{{36d = 540}}}
{{{d = 15}}}
and
(1) {{{q = d - 4}}}
{{{q = 15 - 4}}}
{{{q = 11}}}
and
(2) {{{n = 2d}}}
{{{n = 2*15}}}
{{{n = 30}}}
She has 30 nickels, 15 dimes, and 11 quarters
check:
(3) {{{5n + 1d + 25q = 440}}} (in cents)
{{{5*30 + 15 + 25*11 = 440}}}
{{{150 + 15 + 275 = 440}}}
{{{440 = 440}}}
OK