Question 1009657
Let {{{ a }}} = number of admission tickets sold
Let {{{ b }}} = number of member tickets sold
Let {{{ c }}} = number of student tickets sold
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(1) {{{ a + b + c = 1050 }}}
(2) {{{ 5a + 4b + 2.5c = 4035 }}}
(3) {{{ c = a + 35 }}}
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Multiply both sides of (1) by {{{ 4 }}} and
subtract (2) from (1)
(1) {{{ 4a + 4b + 4c = 4200 }}}
(2) {{{ -5a - 4b - 2.5c = -4035 }}}
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{{{ -a + 1.5c = 165 }}}
{{{ -2a + 3c = 330 }}}
Substitute (3) into this result
{{{ -2a + 3*( a + 35 ) = 330 }}}
{{{ -2a + 3a + 105 = 330 }}}
{{{ a = 225 }}}
and
(3) {{{ c = a + 35 }}}
(3) {{{ c = 225 + 35 }}} 
(3) {{{ c = 260 }}}
and
(1) {{{ a + b + c = 1050 }}}
(1) {{{ 225 + b + 260 = 1050 }}}
(1) {{{ b + 485 = 1050 }}}
(1) {{{ b = 565 }}}
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225 admission tickets were sold
565 member tickets were sold
260 student tickets were sold
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check:
(2) {{{ 5a + 4b + 2.5c = 4035 }}}
(2) {{{ 5*225 + 4*565 + 2.5*260 = 4035 }}}
(2) {{{ 1125 + 2260 + 650 = 4035 }}}
(2) {{{ 4035 = 4035 }}}
OK