Linear Functions: Graphing Solutions & Variables in Context

A local bakery sells cupcakes and cookies. The cost of cupcakes is $2 each and cookies are $1 each. If a customer buys a total of 10 items for $16, how many cupcakes and cookies did they buy? Identify the independent and dependent variables.

• 6 cupcakes and 4 cookies

• 5 cupcakes and 5 cookies

• 7 cupcakes and 3 cookies

• 4 cupcakes and 6 cookies

A school is planning a field trip. The cost per student is $30, and there are fixed costs of $150 for the bus. If 20 students sign up, how much will the total cost be? Graph the situation and interpret the solution.

• $750

• $450

• $900

• $600

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $5 each week, while Jamie saves $10 each week. If they both start with $20, how many weeks will it take for Jamie to have twice as much money as Alex?

• Impossible

• 10 weeks

• 5 weeks

• 3 weeks

A farmer has two types of crops: corn and wheat. He can plant a maximum of 100 acres. Corn requires 2 acres per unit, and wheat requires 1 acre per unit. If he wants to plant 40 units of corn, how many units of wheat can he plant? Identify the dependent and independent variables.

• 50 units of wheat

• 20 units of wheat

• 30 units of wheat

• 10 units of wheat

A gym charges a monthly fee of $30 plus $5 per class attended. If a member attends 8 classes in a month, what is their total cost? Create a system of equations and graph the solution to interpret it.

• $70

• $100

• $80

• $50

A bookstore sells novels for $15 and textbooks for $25. If a customer buys a total of 5 books for $100, how many novels and textbooks did they buy? Write a system of equations to represent this and identify the variables.

• 5 novels and 0 textbooks

• 2 novels and 3 textbooks

• 1 novel and 4 textbooks

• 3 novels and 2 textbooks

A concert hall has a seating capacity of 500. If tickets for the front row are $50 and for the back row are $30, and a total of $15,000 is made from ticket sales, how many tickets were sold for each row? Graph the equations and interpret the results.

• Front row tickets sold: 250, Back row tickets sold: 250

• Front row tickets sold: 0, Back row tickets sold: 500

• Front row tickets sold: 100, Back row tickets sold: 400

• Front row tickets sold: 50, Back row tickets sold: 450

A pizza shop sells small pizzas for $8 and large pizzas for $12. If a customer orders a total of 10 pizzas for $88, how many small and large pizzas did they order? Create a system of equations and identify the dependent and independent variables.

• 5 small pizzas and 5 large pizzas

• 10 large pizzas and 0 small pizzas

• 8 small pizzas and 2 large pizzas

• 6 small pizzas and 4 large pizzas

A charity event sells tickets for $20 each and has a goal of raising $1,000. If they sell 30 tickets, how many more tickets do they need to sell to reach their goal? Graph the situation and interpret the solution.

• 20

• 25

• 10

• 15