Question 747034
Let {{{ n }}} = number of nickels
Let {{{ d }}} = number of dimes
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(1) {{{ n + d = 15 }}}
(2) {{{ 5n + 10d = 120 }}} ( in cents )
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Multiply both sides 0f (1) by {{{ 10 }}}
and subtract (2) from (1)
(1) {{{ 10n + 10d = 150 }}}
(2) {{{ -5n - 10d = -120 }}} 
{{{ 5n = 30 }}}
{{{ n = 6 }}}
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and, since
(1) {{{ n + d = 15 }}}
(1) {{{ 6 + d = 15 }}}
{{{ d = 9 }}}
She has 6 nickels and 9 dimes
check:
(2) {{{ 5n + 10d = 120 }}} 
(2) {{{ 5*6 + 10*9 = 120 }}}
(2) {{{ 30 + 90 = 120 }}}
(2) {{{ 120 = 120 }}}
OK