Question 1111426
Let {{{ a }}} = cost/pound of coffee
Let {{{ b }}} = cost/pound of sugar
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(1) {{{ 8a + 5b = 50.64 }}}
(2) {{{ 12a + 9b = 76.80 }}}
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(1) {{{ 800a + 500b = 5064 }}}
Multiply both sides by {{{ 3 }}}
(1) {{{ 2400a + 1500b = 15192 }}}
and
(2) {{{ 1200a + 900b = 7680 }}}
Multiply both sides of (2) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2400a + 1800b = 15360 }}}
(1) {{{ -2400a - 1500b = -15192 }}}
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{{{ 300b = 168 }}}
{{{ b = .56 }}}
and
(1) {{{ 8a + 5b = 50.64 }}}
(1) {{{ 8a + 5*.56 = 50.64 }}}
(1) {{{ 8a = 50.64 - 2.8 }}}
(1) {{{ 8a = 47.84 }}}
(1) {{{ a = 5.98 }}}
Coffee is $5.98/pound
Sugar is $.56/pound
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check:
(1) {{{ 8a + 5b = 50.64 }}}
(1) {{{ 8*5.98 + 5*.56 = 50.64 }}}
(1) {{{ 47.84 + 2.8 = 50.64 }}}
(1) {{{ 50.64 = 50.64 }}}
OK
You can check (2)