Question 695715
Let {{{ n }}} = number of nickels she has
Let {{{ q }}} = number of quarters she has
given:
(1) {{{ n = q + 8 }}}
(2) {{{ 5n + 25q = 520 }}} ( in cents )
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Substitute (1) into (2)
(2) {{{ 5*( q + 8 ) + 25q = 520 }}} 
(2) {{{ 5q + 40 + 25q = 520 }}}
(2) {{{ 30q = 480 }}}
(2) {{{ q = 48/3 }}}
(2) {{{ q = 16 }}}
and, since
(1) {{{ n = q + 8 }}}
(1) {{{ n = 16 + 8 }}}
(1) {{{ n = 24 }}}
She has 24 nickels and 16 quarters
You made some minor mistake
check answer:
(2) {{{ 5*24 + 25*16 = 520 }}}
(2) {{{ 120 + 400 = 520 }}}
(20 {{{ 520 = 520 }}}
OK