Question 702096
Let {{{ a }}} = number of children's tickets sold
Let {{{ b }}} = number of  adult tickets sold
(1) {{{ a + b = 175 }}}
(2) {{{ 2a + 6b = 750 }}}
--------------------
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2a + 6b = 750 }}}
(1) {{{ -2a - 2b = -350 }}}
{{{ 4b = 400 }}}
{{{ b = 100 }}}
and
(1) {{{ a + b = 175 }}}
(1) {{{ a + 100 = 175 }}}
(1) {{{ a = 75 }}}
75 children's tickets were sold 
check:
(2) {{{ 2*75 + 6*100 = 750 }}}
(2) {{{ 150 + 600 = 750 }}}
(2) {{{ 750= 750 }}}
OK