Question

Write a system of equations to describe the problem situation. Use guess and check to solve the problem. On a weekend, two adult movie tickets and three student tickets cost $28.50. Three adult and two student tickets cost $31.50. What is the price of each ticket? adult ticket $ . student ticket $

Answer 1

The price of an adult movie ticket is $7.00 and the price of a student ticket is $4.50. We derived these prices by setting up a system of equations and solving for the variables A (adult ticket price) and S (student ticket price) algebraically.

Step-by-step explanation:

To write a system of equations for the given problem, we assign variables to the unknowns. Let's let A represent the price of an adult movie ticket and S represent the price of a student ticket. Based on the information provided:

• 2 adult tickets + 3 student tickets = $28.50
• 3 adult tickets + 2 student tickets = $31.50

These statements can be written as the following system of equations:

1. 2A + 3S = 28.50
2. 3A + 2S = 31.50

To solve for A and S using guess and check, we could make educated guesses about the values of A and S and substitute them into the equations to see if they satisfy both equations. However, to solve algebraically, we can use substitution or elimination. Let's use elimination:

1. Multiply the first equation by 3 and the second by 2 to align the coefficients for one of the variables:
2. 6A + 9S = 85.50
3. 6A + 4S = 63.00
4. Subtract the second equation from the first:
5. 5S = 22.50
6. Divide by 5 to find the value of S:
7. S = 4.50
8. Substitute S back into one of the original equations to find A:
9. 2A + 3(4.50) = 28.50
10. 2A = 14.00
11. A = 7.00

Therefore, the adult ticket costs $7.00 and the student ticket costs $4.50.