Solving Systems of Equations: Ticket Cost Word Problem

Published on June 4, 2026

Word-Problem

Learn to solve a word problem involving two systems of linear equations to find the cost of adult and student tickets.

Question

Based on the image provided, here is the step-by-step solution to the math problem.

Jacob’s family bought 4 adult tickets and 2 student tickets to the school play for

. Tatianna’s family bought 3 adult tickets and 3 student tickets for

. How much does each type of ticket cost?

1. Define the variables:
Let

be the cost of one adult ticket.
Let

be the cost of one student ticket.

2. Set up the system of equations based on the information given:

3. Simplify Equation 2:
We can divide every term in Equation 2 by 3 to make it easier to work with:

From this, we can express

in terms of

4. Substitute the expression for into Equation 1:

5. Solve for :

So, an adult ticket costs .

6. Solve for :
Substitute the value of

back into the simplified equation

So, a student ticket costs .

7. Verification:

An adult ticket costs and a student ticket costs .