Question

You receive a $60 gift card to a move theater. a ticket to an afternoon show costs $6 and a ticket to an evening show costs $10. the rules of the gift card state that you can only buy a maximum of 8 total tickets with the card. let x = the number of afternoon tickets and y = the number of evening tickets.

Answer 1

To solve this problem, we can use the constraints given in the question to form equations and then solve the system of equations. We can graph these inequalities on a coordinate plane to find the feasible region and determine the maximum number of afternoon and evening tickets that can be purchased with the gift card.

Step-by-step explanation:

To solve this problem, we can use the constraints given in the question to form equations and then solve the system of equations. Let x represent the number of afternoon tickets and y represent the number of evening tickets.

The cost of the afternoon tickets is $6, so the cost of x afternoon tickets would be 6x.

The cost of the evening tickets is $10, so the cost of y evening tickets would be 10y.

We know that the total cost of the tickets should not exceed $60, so we can form the equation 6x + 10y ≤ 60.

We also know that the total number of tickets should not exceed 8, so we can form the equation x + y ≤ 8.

Now we have a system of linear inequalities:

• 6x + 10y ≤ 60
• x + y ≤ 8

We can graph these inequalities on a coordinate plane to find the feasible region. The feasible region represents the values of x and y that satisfy both inequalities. The feasible region will be a shaded area on the graph.

After graphing the inequalities and finding the feasible region, we can find the maximum number of tickets by looking for the point within the feasible region that maximizes the sum of x and y. This will give us the maximum number of afternoon and evening tickets that can be purchased with the gift card.

I hope this helps! Let me know if you have any further questions.