Finding Intersection Points in Graphing Equations

A local bakery sells cupcakes and cookies. The cost of cupcakes is $2 each and cookies are $1 each. If a customer spends $20, how many cupcakes and cookies could they buy? Graph the equations and find the intersection point.

• Possible combinations include (0 cupcakes, 20 cookies), (1 cupcake, 18 cookies), (2 cupcakes, 16 cookies), ..., (10 cupcakes, 0 cookies).

• (12 cupcakes, -4 cookies)

• (3 cupcakes, 15 cookies)

• (5 cupcakes, 10 cookies)

A school is planning a field trip. The cost per student for the bus is $5 and for the entrance fee is $10. If the total budget is $150, how many students can attend? Graph the equations and identify the intersection point.

• 15 students

• 10 students

• 5 students

• 20 students

A farmer has a total of 100 acres to plant corn and wheat. Corn requires 2 acres per unit and wheat requires 1 acre per unit. If the farmer wants to plant a maximum of 50 units of crops, graph the equations and find the intersection point.

• (50, 0)

• (40, 10)

• (30, 20)

• (60, 0)

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Another company charges $20 plus $0.25 per mile. How many miles would make the costs equal? Graph the equations and identify the intersection point.

• 200 miles

• 300 miles

• 250 miles

• 150 miles

A concert venue has two pricing models. The first charges $15 per ticket, and the second charges a flat fee of $50 for up to 5 tickets. How many tickets would make the total cost the same? Graph the equations and find the intersection point.

• 4

• 5

• 3

• 2

A gym offers two membership plans. Plan A costs $25 per month, while Plan B has a $50 initiation fee and $15 per month. How many months would make the costs equal? Graph the equations and identify the intersection point.

• 5 months

• 10 months

• 3 months

• 7 months

A bookstore sells novels for $10 each and textbooks for $20 each. If a customer spends $100, how many novels and textbooks could they buy? Graph the equations and find the intersection point.

• 12 novels and 1 textbook

• The customer can buy 10 novels and 0 textbooks, or combinations like (8 novels, 1 textbook), (6 novels, 2 textbooks), etc.

• 0 novels and 10 textbooks

• 5 novels and 5 textbooks

A pizza shop sells small pizzas for $8 and large pizzas for $12. If a customer spends $60, how many small and large pizzas can they buy? Graph the equations and identify the intersection point.

• The customer can buy 0 small and 5 large pizzas, 3 small and 2 large pizzas, or 6 small and 0 large pizzas.

• 4 small and 1 large pizza

• 1 small and 3 large pizzas

• 2 small and 4 large pizzas

A charity event sells tickets for $25 each and offers a group discount for $200 for 10 tickets. How many tickets would make the total cost the same? Graph the equations and find the intersection point.

• 8

• 6

• 12

• 10

A landscaping company charges $50 for a basic service and $75 for a premium service. If a customer has a budget of $300, how many services can they afford? Graph the equations and identify the intersection point.

• 7 basic services or 2 premium services

• 6 basic services or 4 premium services, or combinations thereof.

• 5 basic services or 3 premium services

• 4 basic services or 5 premium services