Solving Ticket Sales: Equations and Graphs for 8th Graders

Homer sells adult tickets for $10 and child tickets for $5. If he sells a total of 30 tickets and makes $200, how many adult and child tickets did he sell?

• 20 adult tickets and 10 child tickets

• 15 adult tickets and 15 child tickets

• 10 adult tickets and 20 child tickets

• 5 adult tickets and 25 child tickets

Homer's ticket sales can be represented by the equations x + y = 50 and 10x + 5y = 300, where x is the number of adult tickets and y is the number of child tickets. Solve the system of equations to find the number of each type of ticket sold.

• 10 adult tickets and 40 child tickets

• 20 adult tickets and 30 child tickets

• 5 adult tickets and 45 child tickets

• 15 adult tickets and 35 child tickets

Homer's ticket sales are represented by the equations 2x + 3y = 60 and x + y = 20. Graph these equations to find the point of intersection, which represents the number of adult and child tickets sold.

• (0, 20)

• (5, 15)

• (15, 5)

• (10, 10)

Homer sells tickets for a concert. The total number of tickets sold is 40, and the total revenue is $500. If adult tickets are $15 and child tickets are $10, set up a system of equations to represent this situation and solve for the number of each type of ticket sold.

• 20 adult tickets and 20 child tickets

• 30 adult tickets and 10 child tickets

• 10 adult tickets and 30 child tickets

• 25 adult tickets and 15 child tickets

If Homer sells 20 tickets in total, and the number of adult tickets is twice the number of child tickets, write a system of equations to represent this situation and solve for the number of each type of ticket.

• 15 adult tickets and 5 child tickets

• 12 adult tickets and 6 child tickets

• 8 adult tickets and 12 child tickets

• 10 adult tickets and 10 child tickets

Homer's ticket sales can be modeled by the equations 4x + 2y = 80 and x + y = 20. Identify the variables and constants in these equations and solve for x and y.

• x = 0, y = 20

• x = 20, y = 0

• x = 15, y = 5

• x = 10, y = 10

Homer sells tickets for a school play. If he sells 25 tickets and collects $150, with adult tickets priced at $8 and child tickets at $5, create a system of equations to find out how many of each type of ticket he sold.

• 5 adult tickets and 20 child tickets

• 20 adult tickets and 5 child tickets

• 10 adult tickets and 15 child tickets

• 15 adult tickets and 10 child tickets

Homer's ticket sales are represented by the equations 3x + 4y = 120 and x + y = 30. Graph these equations and identify the solution that represents the number of adult and child tickets sold.

• Adult tickets: 15, Child tickets: 15

• Adult tickets: 5, Child tickets: 25

• Adult tickets: 10, Child tickets: 20

• Adult tickets: 0, Child tickets: 30

If Homer sells tickets for a sports event and the total number of tickets sold is 60, with adult tickets priced at $12 and child tickets at $6, write a system of equations to represent this situation and solve for the number of each type of ticket sold.

• x + y = 60 and 10x + 6y = total revenue

• The number of adult tickets sold is x and child tickets sold is y, where x + y = 60 and 12x + 6y = total revenue.

• x + y = 50 and 12x + 8y = total revenue

• x + y = 60 and 12x + 5y = total revenue