Question 638539
Let {{{ a }}} = number of adult tickets sold
Let {{{ c }}} = number of children's tickets sold
given:
(1) {{{ a + c = 400 }}}
(2) {{{ 25a + 15c = 7200 }}}
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Multiply both sides of (1) by {{{ 15 }}}
and subtract (1) from (2)
(2) {{{ 25a + 15c = 7200 }}}
(1) {{{ -15a - 15c = -6000 }}}
{{{ 10a  = 1200 }}}
{{{ a = 120 }}}
and, since
(1) {{{ a + c = 400 }}}
(1) {{{ 120 + c = 400 }}}
(1) {{{ c = 280 }}}
120 adult tickets were sold
280 children's tickets were sold
check:
(2) {{{ 25*120 + 15*280 = 7200 }}}
(2) {{{ 3000 + 4200 = 7200 }}}
(2) {{{ 7200 = 7200 }}}
OK