Algebra Question

Question

The number of students attending the spring play was 100 more than the number of adults attending. Student tickets cost $4 each and adult tickets cost $6 each. A total of $4400 was collected. How many students and adults attended the play? Write a system of equations that represents this situation and solve. Show your work!

Answer 1

We need to create a system of equations based on the information we're given. Let's start with naming the variables.

Let S= Student Tickets and A = Adult Tickets

The first sentence gives us an equation of S = 100 + A

The second sentence gives us an equation of 4S + 6A = 4400

Now that we have two equations we can solve.

Start by substituting S= 100 + A into the second equation.

4(100 + A) + 6A = 4400

400 + 4A + 6A = 4400

400 + 10A = 4400

10A = 4000

A = 400

If A = 400, then S = 500.

Answer 2

Let A = number of adults, then the number of students is A+100

6(A) + 4(A+100) = 4400

6A + 4A +400 = 4400

10A= 4000

A = 400 the number of adults

A+100 = 500 the number of students