Question 724056
Let {{{ a }}} = number of rs. 100 tickets sold
Let {{{ b }}} = number of rs. 120 tickets sold
given:
(1) {{{ a + b = 200 }}}
(2) {{{ 100a + 120b = 22600 }}}
--------------------------
(2) {{{ 10a + 12b = 2260 }}}
(2) {{{ 5a + 6b = 1130 }}}
Multiply both sides of (1) by {{{ 5 }}}
and subtract (1) from (2)
(2) {{{ 5a + 6b = 1130 }}}
(1) {{{ -5a - 5b = -1000 }}}
{{{ b = 130 }}}
and, since
(1) {{{ a + b = 200 }}}
(1) {{{ a = 70 }}}
70 rs. 100 tickets were sold
130 rs. 120 tickets were sold
check answer:
(2) {{{ 100a + 120b = 22600 }}}
(2) {{{ 100*70 + 120*130 = 22600 }}}
(2) {{{ 7000 + 15600 = 2260 }}}
(2) {{{ 2260 = 2260 }}}
OK