Question 577694
Let {{{a}}} = number of adult tickets sold
Let {{{c}}} = number of children's tickets sold
Let {{{s}}} = number of senior's tickets sold
given:
(1) {{{ a + c + s = 1800 }}}
(2) {{{ 5a + 2.5c + 4s = 7425 }}}
(3) {{{ c + s = 900 }}}
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Subtract (3) from (1)
(1) {{{ a + c + s = 1800 }}}
(3) {{{ -c - s = -900 }}}
{{{ a = 900 }}}
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and
(3) {{{ c + s = 900 }}}
(3) {{{ c = 900 - s }}}
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Substitute into (2)
(2) {{{ 5a + 2.5c + 4s = 7425 }}}
(2) {{{ 5*900 + 2.5*( 900 - s ) + 4s = 7425 }}}
(2) {{{ 4500 + 2250 - 2.5s + 4s = 7425 }}}
(2) {{{ 1.5s = 7425 - 4500 - 2250 }}}
(2) {{{ 1.5s = 675 }}}
(2) {{{ s = 675/1.5 }}}
(2) {{{ s = 450 }}}
and, since
(3) {{{ c = 900 - s }}}
(3) {{{ c = 900 - 450 }}}
(3) {{{ c = 450 }}}
900 adult tickets were sold
450 children's tickets were sold
450 senior's tickets were sold