Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75.

Question

Write a system of equations to represent the situation.

Answer 1

Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75.

Ticket for an adults = $7.25

Ticket for a student = $5.50

Let number of adults be A

Let number of students be S

Then, A + S = 8    (number of people in group)

And, A*7.25 + S*5.50 = 52.75    (sum of individual costs = total cost)

Substituting for A = 8 - S, from 1st eqn, into 2nd eqn gives us,

(8 - S)*7.25 + S*5.5 = 52.75

58 - 7.25S + 5.5S = 52.75

58 - 1.75S = 52.75

58 - 52.75 = 1.75S

S = 5.25/1.75 = 3

A = 8 - S = 5

There are 5 adults and 3 students