Question 769337
Let {{{ c }}} = number of cases of coffee
Let {{{ t }}} = number of cases of tea
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(1) {{{ c + t = 250 }}}
(2) {{{ 12c + 8t = 2600 }}}
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Multiply both sides of (1) by {{{ 8 }}}
and subtract (1) from (2)
(2) {{{ 12c + 8t = 2600 }}}
(1) {{{ -8c - 8t = -2000 }}}
{{{ 4c = 600 }}}
{{{ c = 150 }}}
and, since
(1) {{{ c + t = 250 }}}
(1) {{{ 150 + t = 250 }}}
(1) {{{ t = 100 }}}
150 = number of cases of coffee
100 = number of cases of tea
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check:
(2) {{{ 12c + 8t = 2600 }}}
(2) {{{ 12*150 + 8*100 = 2600 }}}
(2) {{{ 1800 + 800 = 2600 }}}
(2) {{{ 2600 = 2600 }}}
OK