Model with systems

Question

Student tickets for school music are $5 each and adult tickets are $12 each. During closing night, total ticket sales earned $1960. The difference between student and adult tickets sold was 52 tickets. How many student and adult tickets were sold?

Answer 1

You are asked to find two numbers - no.of student tickets sold, 'X' and no. of adult tickets sold 'Y'. To find two variables, you must have a system of two equations. So, that's what we will do.

First make use of the statement that the "total ticket sales earned $1960". Given the prices of each student and adult ticket, the total sales is

5X + 12Y = 1960

The second equation is set up using the statement "The difference between student and adult tickets sold was 52 tickets".

X - Y = 52

You can solve the two equations in a couple of different ways. You should be able to get

X = 100

Y = 48