Question 630165
Let {{{ a }}} = the number of 23 cent stamps
Let {{{ b }}} = the number of 41 cent stamps
Let {{{ c }}} = the number of 80 cent stamps
given:
(1) {{{ 23a + 41b + 80c = 3150 }}} ( in cents )
(2) {{{ a = b + 2 }}}
(3) {{{ c = b/2 + 5 }}}
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Substitute (2) and (3) into (1)
(1) {{{ 23*( b + 2 ) + 41b + 80*( b/2 + 5 ) = 3150 }}}
(1) {{{ 23b + 46 + 41b + 40b + 400 = 3150 }}}
(1) {{{ 23b + 41b + 40b = 3150 - 46 - 400 }}}
(1) {{{ 104b = 2704 }}}
(1) {{{ b = 26 }}}
and, since
(2) {{{ a = b + 2 }}}
(2) {{{ a = 26 + 2 }}}
(2) {{{ a = 28 }}}
and
(3) {{{ c = b/2 + 5 }}}
(3) {{{ c = 26/2 + 5 }}}
(3) {{{ c = 13 + 5 }}}
(3) {{{ c = 18 }}}
There were 28 of the 23 cent stamps
There were 26 of the 41 cent stamps
There were 18 of the 80 cent stamps
check:
(1) {{{ 23a + 41b + 80c = 3150 }}}
(1) {{{ 23*28 + 41*26 + 80*18 = 3150 }}}
(1) {{{ 644 + 1066 + 1440 = 3150 }}}
(1) {{{ 3150 = 3150 }}}
OK