Question 1040717
Let {{{ a }}} = number of 3 cent stamps
Let {{{ b }}} = number of 7 cent stamps
Let {{{ c }}} = number of 12 cent stamps
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(1) {{{ a = b - 5 }}}
(2) {{{ c = (1/2)*b }}}
(3) {{{ 3a + 7b + 12c = 273 }}} ( in cents )
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Substitute (1) and (2) into (3)
(3) {{{ 3*( b - 5 ) + 7b + 12*( b/2 ) = 273 }}}
(3) {{{ 3b - 15 + 7b + 6b = 273 }}}
(3) {{{ 16b  = 288 }}}
(3) {{{ b = 18 }}}
and
(1) {{{ a = b - 5 }}}
(1) {{{ a = 18 - 5 }}}
(1) {{{ a = 13 }}}
and
(2) {{{ c = (1/2)*b }}}
(2) {{{ c = (1/2)*18 }}}
(2) {{{ c = 9 }}}
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The number of 3 cent stamps is 13
The number of 7 cent stamps is 18
The number of 12 cent stamps is 9
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check:
(3) {{{ 3a + 7b + 12c = 273 }}}
(3) {{{ 3*13 + 7*18 + 12*9 = 273 }}}
You can verify this equation