Tickets cost $8 for an adult and $5 for student. The total revenue for 1 performance was $1122, with 32 more students than adults in the audience.

Question

Write a linear system that models the situation, and then solve the linear system 

Answer 1

Lets use A for the number of adult attendees and S for the number of student attendees...

 

Thus we have that the revenue 1122=8A+5S, we also know that S=A+32, since there were 32 more students than adults.

 

Substituting the value of S=A+32 into the revenue equation will give us a linear equation in the single variable A, which can be easily solved to find the number of adults...adding 32 to this value will give the number of students:

 

1122=8A+5(A+32)= 13A+160....so A=(1122-160)/13= 74...and thus S=74+32=106.

 

Hope that helps!