Question 657292
Let {{{ n }}} = number of nickels
Let {{{ d }}} = number of dimes
Let {{{ q }}} = number of quarters
given:
(1) {{{ d = n + 9 }}}
(2) {{{ q = d + 21 }}}
(3) {{{ 5n + 10d + 25q = 1000 }}} ( in cents )
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From (1):
(1) {{{ n = d - 9 }}}
Substitute (1) and (2) into (3)
(3) {{{ 5*( d - 9 ) + 10d + 25*( d + 21 ) = 1000 }}} 
(3) {{{ 5d - 45 + 10d + 25d + 525 = 1000 }}}
(3) {{{ 40d = 1000 - 525 + 45 }}}
(3) {{{ 40d = 520 }}}
(3) {{{ d = 13 }}}
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and
(1) {{{ n = d - 9 }}}
(1) {{{ n = 13 - 9 }}}
(1) {{{ n = 4 }}}
and
(2) {{{ q = d + 21 }}}
(2) {{{ q = 13 + 21 }}}
(2) {{{ q = 34 }}}
She returned
4 nickels
13 dimes
34 quarters
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check:
(3) {{{ 5*4 + 10*13 + 25*34 = 1000 }}}
(3) {{{ 20 + 130 + 850 = 1000 }}}
(3) {{{ 1000 = 1000 }}}
OK