Question 879045
Let {{{ a }}} = cost of a vegetarian special in dollars
Let {{{ b }}} = cost of a chicken special in dollars
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(1) {{{ 32a + 40b = 544 }}}
(2) {{{ 28a + 36b = 484 }}}
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Multiply both sides of (1) by {{{ 28/32 }}}
(1 ){{{ (28/32)*32a + (28/32)*40b = (28/32)*544 }}}
(1) {{{ (7/8)*32a + (7/8)*40b = (7/8)*544 }}}
(1) {{{ 28a + 35b = 476 }}}
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Subtract (1) from (2)
(2) {{{ 28a + 36b = 484 }}}
(1) {{{ -28a - 35b = -476 }}}
{{{ b = 8 }}}
and, since
(1) {{{ 32a + 40*8 = 544 }}}
(1) {{{ 32a + 320 = 544 }}}
(1) {{{ 32a = 224 }}}
(1) {{{ a = 7 }}}
The vegetarian special costs $7 each
The chicken special costs $8 each