Graphing Equations: Find Intersection Points in Real-Life Scenarios

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 identify the intersection point.

• The customer can buy various combinations such as 10 cupcakes and 0 cookies, or 0 cupcakes and 20 cookies.

• 8 cupcakes and 8 cookies

• 15 cupcakes and 5 cookies

• 5 cupcakes and 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 $100, how many students can attend? Graph the equations and find the intersection point.

• 8

• 10

• 6

• 4

Two friends are saving money to buy a video game. Friend A saves $3 a week, while Friend B saves $5 a week. If they both start with $10, how many weeks will it take for them to have the same amount saved? Graph the equations and identify the intersection point.

• 0 weeks

• 3 weeks

• 2 weeks

• 1 week

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 total of 50 units, how many units of each can he plant? Graph the equations and find the intersection point.

• 30 units of corn and 20 units of wheat

• 50 units of corn and 0 units of wheat

• 40 units of corn and 10 units of wheat

• 25 units of corn and 25 units of wheat

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Another company charges a flat fee of $20 plus $0.25 per mile. At what distance do both companies charge the same amount? Graph the equations and identify the intersection point.

• 150 miles

• 300 miles

• 200 miles

• 250 miles

A concert venue has a seating capacity of 500. If tickets for the front row are $50 each and for the back row are $30 each, how many tickets can be sold if the total revenue must be $15,000? Graph the equations and find the intersection point.

• 400 mixed tickets

• 250 front row tickets

• 300 back row tickets

• 500 back row tickets

A gym offers two membership plans. Plan A costs $40 per month and Plan B costs $30 per month plus a one-time fee of $100. After how many months will both plans cost the same? Graph the equations and identify the intersection point.

• 8 months

• 12 months

• 10 months

• 5 months

A bookstore sells novels for $12 each and textbooks for $20 each. If a customer spends $120, how many novels and textbooks could they buy? Graph the equations and find the intersection point.

• (2 novels, 4 textbooks)

• (3 novels, 5 textbooks)

• Possible combinations are (0 novels, 6 textbooks), (5 novels, 3 textbooks), (10 novels, 0 textbooks).

• (8 novels, 1 textbook)

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.

• (4 small, 1 large)

• (2 small, 4 large)

• (1 small, 3 large)

• Possible combinations are (0 small, 5 large), (3 small, 2 large), (6 small, 0 large).

A charity is organizing a fundraiser. They sell tickets for $10 each and snacks for $5 each. If they want to raise $500, how many tickets and snacks do they need to sell? Graph the equations and find the intersection point.

• They can sell 25 tickets and 25 snacks.

• They can sell 10 tickets and 80 snacks.

• They can sell 75 tickets and 10 snacks.

• They can sell 50 tickets and 0 snacks, or 0 tickets and 100 snacks, among other combinations.