Question 248836
Let {{{x}}} = number of adult tickets sold
Let {{{y}}} = number of children's tickets sold
given:
{{{410x + 270y = 33130}}} (in cents)
(1) {{{41x + 27y = 3313}}}
(2) {{{x + y = 89}}}
Multiply both sides of (2) by {{{27}}}
and subtract from (1)
(1) {{{41x + 27y = 3313}}}
(2) {{{-27x - 27y = -2403}}}
{{{14x = 910}}}
{{{x = 65}}}
and, since
{{{x + y = 89}}}
{{{65 + y = 89}}}
{{{y = 89 - 65}}}
{{{y = 24}}}
65 adult tickets and 24 children's tickets were sold
check:
(1) {{{41x + 27y = 3313}}}
{{{41*65 + 27*24 = 3313}}}
{{{2665 + 648 = 3313}}}
{{{3313 = 3313}}}
OK