Question

Tickets for the senior play cost $4. 00 for adults and $2. 00 for students. This year there

were 600 tickets sold, and the class made $1900. Write and solve a system to determine

how many of each type ticket were sold.

Answer 1

250 student tickets were sold

350 adult tickets were sold

Explanation:

• Before we can begin the solving the system, we need to determine which equations we can use and which variables.

First equation:

• We can allow A to represent the number of adult tickets sold and S to represent the number of student tickets sold.

We know that the revenues earned from the adult and student tickets equals the total revenue:

(adult ticket price * quantity) + (student ticket price * quantity) = total revenue.

Thus, the first equation in our system is given by:

4A + 2S = 1900

Second equation:

We also know that the sum of the adult and student tickets equals the total number of tickets sold:

adult ticket total quantity + student ticket total quantity = total tickets sold

Thus, the second equation in our system is given:

A + S = 600

Method to solve: Substitution

Before we begin solving by substitution, we can isolate A in the second equation:

(A + S = 600) - S

A = -S + 600

Solving for S, the number of student tickets sold:

Now we can solve for S by substituting -S + 600 for A in the first equation (i.e., 4A + 2S = 1900):

4(-S + 600) + 2S = 1900

-4S + 2400 + 2S = 1900

(-2S + 2400 = 1900) - 2400

(-2S = -500) / -2

S = 250

Thus, 250 student tickets were sold.

Solving for A, the number of adult tickets sold:

Now we can plug in 250 for S in the second equation (i.e., A + S = 600) to solve for A:

(A + 250 = 600) - 250

A = 350

Thus, 350 adult tickets were sold.