Question 725854
Let {{{ a }}} = number of tickets sold in advance
Let {{{ b }}} = number sold at the door
given:
(1) {{{ a + b = 100 }}}
(2) {{{ 1*a + 1.5*b = 120 }}}
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(2) {{{ 10a + 15b = 1200 }}}
(2) {{{ 2a + 3b = 240 }}}
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2a + 3b = 240 }}}
(1) {{{ -2a - 2b = -200 }}}
{{{ b = 40 }}}
and, since
(1) {{{ a + b = 100 }}}
(1) {{{ a + 40 = 100 }}}
(1) {{{ a = 60 }}}
60 tickets were sold in advance
40 tickets were sold at the door
check:
(2) {{{ 1*a + 1.5*b = 120 }}}
(2) {{{ 1*60 + 1.5*40 = 120 }}}
(2) {{{ 60 + 60 = 120 }}}
(2) {{{ 120 = 120 }}}
OK