Question 1094425
Let {{{ a }}} = number of adult tickets sold
Let {{{ b }}} = number of children's tickets sold
Let {{{ c }}} = number of senior tickets sold
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(1) {{{ a + b + c = 990 }}}
(2) {{{ 13a + 9b + 5c = 9858 }}}
(3) {{{ a + b = 2c + 222 }}}
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There are 3 equations and 3 unknowns, so it's solvable
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(3) {{{ a + b - 2c = 222 }}}
Subtract (3) from (1)
(1) {{{ a + b + c = 990 }}}
(3) {{{ -a - b + 2c = -222 }}}
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{{{ 3c = 768 }}}
{{{ c = 256 }}}
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(2) {{{ 13a + 9b + 5*256 = 9858 }}}
(2) {{{ 13a + 9b + 1280 = 9858 }}}
(2) {{{ 13a + 9b = 8578 }}}
and
(1) {{{ a + b + c = 990 }}}
(1) {{{ a + b + 256 = 990 }}}
(1) {{{ a + b = 734 }}}
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Multiply both sides of (1) by {{{ 9 }}}
and subtract (1) from (2)
(2) {{{ 13a + 9b = 8578 }}}
(1) {{{ -9a - 9b = -6606 }}}
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{{{ 4a = 1972 }}}
{{{ a = 493 }}}
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and
(3) {{{ a + b - 2c = 222 }}}
(3) {{{ 493 + b - 2*256 = 222 }}}
(3) {{{ 493 + b - 512 = 222 }}}
(3) {{{ b - 19 = 222 }}}
(3) {{{ b = 241 }}}
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The number of adult tickets sold was 493
The number of children's tickets sold was 241
The number of senior tickets sold was 256
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Check answers
(1) {{{ a + b + c = 990 }}}
(1) {{{ 493 + 241 + 256 = 990 }}}
(1) {{{ 990 = 990 }}}
You can check (2) and (3)
Get another opinion if needed