Question 837702
x = student ticket
y = Faculty ticket

Equations from the Problem

{{{x+y=200}}} eq.1
{{{20x+50y=5200}}} eq.2

substitution method:

{{{x=200-y}}} eq.3

substitute eq.3 to eq. 2
{{{20(200-y)+50y=5200}}}
{{{4000-20y+50y=5200}}}
{{{30y=5200-4000}}}
{{{30y=1200}}}
{{{30y/30=1200/30}}}
.
{{{highlight (y=40)}}}

substitute the value of y to eq.3

{{{x=200-40}}} 
.
{{{highlight (x=160)}}}