Question 665485
Let {{{n }}} = number of nickels she has
Let {{{ d }}} = number of dimes she has
given:
(1) {{{ n + d = 107 }}}
(2) {{{ 5n + 10d = 865 }}} ( in cents )
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Multiply both sides of (1) by {{{ 5 }}}
and subtract (1) from (2)
(2) {{{ 5n + 10d = 865 }}} 
(1) {{{ -5n - 5d = 535 }}}
{{{ 5d = 330 }}}
{{{ d = 66 }}}
and, since
(1) {{{ n + d = 107 }}}
(1) {{{ n + 66 = 107 }}}
(1) {{{ n = 41 }}}
She has 41 nickels and 66 dimes
check:
(2) {{{ 5*41 + 10*66 = 865 }}} 
(2) {{{ 205 + 660 = 865 }}}
(2) {{{ 865 = 865 }}}
OK