The very busy Freshman class is selling tickets for an upcoming field hockey game. The class sells 20 more student tickets than adult tickets. The adult tickets cost $4 and the student tickets cost $2. The class made a total of $280 from ticket sales. How many of each type of ticket did they sell? Elaborate and clarify your reasoning.

1a. Define the variables in this system

b. Create equations to describe the relationships in this system between the variables

60 student tickets and 40 adult tickets were sold

Step-by-step explanation:

Let s represent student tickets and a adult tickets, then the system of equations can be written as

s - a = 20 → (1)

2s + 4a = 280 → (2)

Multiply (1) by 4 and add to (2) to eliminate a

4s - 4a = 80 → (3)

Add (2) and (3) term by term

6s = 360 (divide both sides by 6)

s = 60

Substitute s = 60 into (1)

60 - a = 20 (subtract 60 from both sides)

- a = - 40 (multiply both sides by - 1)

a = 40

Thus

60 student and 40 adult tickets were sold.