Question 957470
Let {{{ a }}} = the cost in dollars of 1 hot dog
Let {{{ b }}} = the cost in dollars of 1 hamburger
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given:
(1) {{{ 3a + 2b = 7.5 }}}
(2) {{{ 2a + 3b = 8.75 }}}
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Multiply both sides of (1) by {{{ 2 }}}
Multiply both sides of (2) by {{{ 3 }}}
Subtract (1) from (2)
(2) {{{ 6a + 9b = 26.25 }}}
(1) {{{ -6a - 4b = -15 }}}
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{{{ 5b = 11.25 }}}
{{{ b = 2.25 }}}
and
(1) {{{ 3a + 2*2.25 = 7.5 }}}
(1) {{{ 3a = 7.5 - 4.5 }}}
(1) {{{ 3a = 3 }}}
(1) {{{ a = 1 }}}
1 hot dog costs $1
1 hamburger costs $2.25
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check:
(1) {{{ 3*1 + 2*2.25 = 7.5 }}}
(1) {{{ 3 + 4.5 = 7.5 }}}
(1) {{{ 7.5 = 7.5 }}}
and
(2) {{{ 2*1 + 3*2.25 = 8.75 }}}
(2) {{{ 2 + 6.75 = 8.75 }}}
(2) {{{ 8.75 = 8.75 }}}
OK