Question 1022023
Let {{{ a }}} = the price of an adult's ticket
Let {{{ b }}} = the price of a child's ticket
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(1) {{{ 3a + 4b = 108 }}}
(2) {{{ 2a + 3b = 76 }}}
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Multiply both sides of (1) by {{{ 2 }}}
Multiply both sides of (2) by {{{ 3 }}}
Subtract (1) from (2)
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(2) {{{ 6a + 9b = 228 }}}
(1) {{{ -6a - 8b = -216 }}}
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{{{ b = 12 }}}
and
(1) {{{ 3a + 4b = 108 }}}
(1) {{{ 3a + 4*12 = 108 }}}
(1) {{{ 3a + 48 = 108 }}}
(1) {{{ 3a = 60 }}}
(1) {{{ a = 20 }}}
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The price of an adult's ticket is $20
The price of a child's ticket is $12
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check:
(2) {{{ 2a + 3b = 76 }}}
(2) {{{ 2*20 + 3*12 = 76 }}}
(2) {{{ 40 + 36 = 76 }}}
(2) {{{ 76 = 76 }}}
OK