Question 681003
Let {{{ q }}} = number of quarters he has
Let {{{ d }}} = number of dimes he has
Let {{{ n }}} = number of nickels he has
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given:
(1) {{{ q = 2n }}}
(2) {{{ d = n + 3}}}
(3) {{{ 25q + 10d + 5n = 420 }}} ( in cents )
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Substitute (1) and (2) into (3)
(3) {{{ 25*(2n) + 10*(n + 3) + 5n = 420 }}}
(3) {{{ 50n + 30 + 10n + 5n = 420 }}}
(3) {{{ 65n = 390}}}
(3) {{{ n = 6 }}}
and
(1) {{{ q = 2n }}}
(1) {{{ q = 2*6 }}}
(1) {{{ q = 12 }}}
and
(2) {{{ d = n + 3}}}
(2) {{{ d = 6 + 3}}}
(2) {{{ d = 9 }}}
Mark has 12 quarters, 9 dimes, and 6 nickels
check:
(3) {{{ 25q + 10d + 5n = 420 }}}
(3) {{{ 25*12 + 10*9 + 5*6 = 420 }}}
(3) {{{ 300 + 90 + 30 = 420 }}}
(3) {{{ 420 = 420 }}}
OK