Question 1112323
Let {{{ a }}} = number of chidren's tickets sold
Let {{{ b }}} = number of student tickets sold
Let {{{ c }}} = number of adult tickets sold
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(1) {{{ a + b + c = 800 }}}
(2) {{{ 3a + 5b + 8c = 4750 }}}
(3) {{{ c = 2a + 50 }}}
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Plug (3) into (1)
(1) {{{ a + b + 2a + 50 = 800 }}}
(1) {{{ 3a + b = 750 }}}
Plug (3) into (2)
(2) {{{ 3a + 5b + 8*( 2a + 50 ) = 4750 }}}
(2) {{{ 3a + 5b + 16a + 400 = 4750 }}}
(2) {{{ 19a + 5b = 4350 }}}
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Multiply both sides of (1) by {{{ 5 }}} and
subtract (1) from (2)
(2) {{{ 19a + 5b = 4350 }}}
(1) {{{ -15a - 5b = -3750 }}}
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{{{ 4a = 600 }}}
{{{ a = 150 }}}
and
(3) {{{ c = 2a + 50 }}}
(3) {{{ c = 2*150 + 50 }}}
(3) {{{ c = 350 }}}
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(1) {{{ a + b + c = 800 }}}
(1) {{{ 150 + b + 350 = 800 }}}
(1) {{{ b = 300 }}}
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150 children's 
300 students
350 adults
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check:
(2) {{{ 3a + 5b + 8c = 4750 }}}
(2) {{{ 3*150 + 5*300 + 8*350 = 4750 }}}
(2) {{{ 450 + 1500 + 2800 = 4750 }}}
(2) {{{ 4750 = 4750 }}}
You can check (1) and (3)