Question 1087816
(1) {{{ 5n + 10d + 25q = 8800 }}} ( in cents )
(2) {{{ q = 2d }}}
(3) {{{ n + d + q = 500 }}}
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Multiply both sides of (3) by {{{ 5 }}} and
subtract (3) from (1)
(1) {{{ 5n + 10d + 25q = 8800 }}} 
(3) {{{ -5n - 5d - 5q = 2500 }}}
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{{{ 5d + 20q = 6300 }}}
{{{ d + 4q = 1260 }}}
Plug (2) into this result
{{{ d + 4*2d = 1260 }}}
{{{ 9d = 1260 }}}
{{{ d = 140 }}}
and
(2) {{{ q = 2d }}}
(2) {{{ q = 280 }}}
and
(3) {{{ n + d + q = 500 }}}
(3) {{{ n + 140 + 280 = 500 }}}
(3) {{{ n = 500 - 420 }}}
(3) {{{ n = 80 }}}
There are 80 nickels
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check:
(1) {{{ 5n + 10d + 25q = 8800 }}}
(1) {{{ 5*80 + 10*140 + 25*280 = 8800 }}}
(1) {{{ 400 + 1400 + 7000 = 8800 }}}
(1) {{{ 8800 = 8800 }}}
OK