Question 569084
Let {{{n}}} = number of nickels
Let {{{q}}} = number of quarters
given:
(1) {{{ n + q = 28 }}}
(2) {{{ 5n + 25q = 360 }}} ( in cents )
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Multiply both sides of (1) by {{{5}}}
and subtract (1) from (2)
(2) {{{ 5n + 25q = 360 }}}
(1) {{{ -5n - 5q = 140 }}}
{{{ 20q = 220 }}}
{{{ q = 11 }}}
and, since
(1) {{{ n + q = 28 }}}
(1) {{{ n + 11 = 28 }}}
(1) {{{ n = 17 }}}
She has 17 nickels and 11 quarters