Question 547270
Let {{{n}}} = number of nickels
Let {{{d}}} = number of dimes
Let {{{q}}} = number of quarters
given:
(1) {{{ q = 2d }}}
(2) {{{ q = 3n }}}
(3) {{{ 5n + 10d + 25q = 190 }}} ( in cents )
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From (1)
(1) {{{ 5q = 10d }}}
(3) {{{ 5n + 5q + 25q = 190 }}} 
and, from (2)
(2) {{{ n = q/3 }}}
(3) {{{ (5/3)*q + 5q + 25q = 190 }}} 
Multiply both sides by {{{3}}}
(3) {{{ 5q + 15q + 75q = 570 }}}
(3) {{{ 95q = 570 }}}
(3) {{{ q = 6 }}}
and
(1) {{{ d = q/2 }}}
(1) {{{ d = 3 }}}
and
{{{ n = q/3 }}}
{{{ n = 2 }}}
She has 2 nickels, 3 dimes, and 6 quarters
check answer:
(3) {{{ 5*2 + 10*3 + 25*6 = 190 }}}
(3) {{{ 10 + 30 + 150 = 190 }}}
(3) {{{ 190 = 190 }}}
OK