Question 1087815
(1) {{{ n + d + q = 105 }}}
(2) {{{ 5n + 10d + 25q = 840 }}} ( in cents )
(3) {{{ d = 2q + 3 }}}
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Multiply both sides of (1) by {{{ 5 }}} and
subtract (1) from (2)
(2) {{{ 5n + 10d + 25q = 840 }}}
(1) {{{ -5n - 5d - 5q = -525 }}}
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{{{ 5d + 20q = 315 }}}
{{{ d + 4q = 63 }}}
Plug (3) into this result
{{{ 2q + 3 + 4q = 63 }}}
{{{ 6q = 60 }}}
{{{ q = 10 }}}
and
(3) {{{ d = 2q + 3 }}}
(3) {{{ d = 2*10 + 3 }}}
(3) {{{ d = 23 }}}
and
(1) {{{ n + d + q = 105 }}}
(1) {{{ n + 23 + 10 = 105 }}}
(1) {{{ n + 33 = 105 }}}
(1) {{{ n = 72 }}}
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72 nickels
23 dimes
10 quarters
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check:
(2) {{{ 5n + 10d + 25q = 840 }}} 
(2) {{{ 5*72 + 10*23 + 25*10 = 840 }}} 
(2) {{{ 360 + 230 + 250 = 840 }}}
(2) {{{ 840 = 840 }}}
OK