Question 951383
Let {{{ n }}} = number of nickels
Let {{{ d }}} = number of dimes
Let {{{ q }}} = number of quarters
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(1) {{{ d = 6q }}}
(2) {{{ n = q + 8 }}}
(3) {{{ 5n + 10d + 25q = 940 }}} ( in cents )
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Substitute (1) and (2) into (3)
(3) {{{ 5*( q + 8 ) + 10*6q + 25q = 940 }}}
(3) {{{ 5q + 40 + 60q + 25q = 940 }}}
(3) {{{ 90q = 900 }}}
(3) {{{ q = 10 }}}
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(1) {{{ d = 6q }}}
(1) {{{ d = 6*10 }}}
(1) {{{ d = 60 }}}
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(2) {{{ n = q + 8 }}}
(2) {{{ n = 10 + 8 }}}
(2) {{{ n = 18 }}}
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There are:
18 nickels
60 dimes
10 quarters
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check:
(3) {{{ 5n + 10d + 25q = 940 }}}
(3) {{{ 5*18 + 10*60 + 25*10 = 940 }}}
(3) {{{ 90 + 600 + 250 = 940 }}}
(3) {{{ 940 = 940 }}}
OK