Question 538164
Let {{{n}}} = number of nickels
Let {{{d}}} = number of dimes
given:
(1) {{{ n + d = 45 }}}
(2) {{{ 5n + 10d = 360 }}}
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Multiply both sides of (1) by {{{5}}}
and subtract (1) from (2)
(2) {{{ 5n + 10d = 360 }}}
(1) {{{ -5n - 5d = -225 }}}
{{{ 5d = 135 }}}
{{{ d = 27 }}}
and, since
(1) {{{ n + d = 45 }}}
(1) {{{ n + 27 = 45 }}}
(1) {{{ n = 45 - 27 }}}
(1) {{{ n = 18 }}}
She had 18 nickels and 27 dimes
check:
(2) {{{ 5*18 + 10*27 = 360 }}}
(2) {{{ 90 + 270 = 360 }}}
(2) {{{ 360 = 360 }}}
OK