Question 705935
Let {{{ n }}} = number of nickels she has
Let {{{ d }}} = number of dimes she has
given:
(1) {{{ n + d = 48 }}}
(2) {{{ 5n + 10d = 450 }}} ( in cents )
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Multiply both sides of (1) by {{{ 5 }}}
and subtract (1) from (2)
(2) {{{ 5n + 10d = 450 }}} 
(1) {{{ -5n - 5d = -240 }}}
{{{ 5d = 210 }}}
{{{ d = 42 }}}
and, since
(1) {{{ n + d = 48 }}}
(1) {{{ n + 42 = 48 }}}
(1) {{{ n = 6 }}}
The number of nickels she has is 6
The number of dimes she has is 42
check answer:
(2) {{{ 5*6 + 10*42 = 450 }}} 
(2) {{{ 30 + 420 = 450 }}}
(2) {{{ 450 = 450 }}}
OK