Graphing and Solving Linear Equations: Grade 8 Challenges

A local bakery sells cupcakes and cookies. Each cupcake costs $2 and each cookie costs $1. If the bakery sells a total of 50 items for $80, how many cupcakes and cookies did they sell? Graph the equations to find the solution.

• 40 cupcakes and 10 cookies

• 20 cupcakes and 30 cookies

• 25 cupcakes and 25 cookies

• 30 cupcakes and 20 cookies

A school is planning a field trip. The cost per student is $15 for transportation and $10 for admission. If 30 students are going, how much will the total cost be? Write the equation and graph it to visualize the total cost.

• $900

• $750

• $600

• $500

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $5 a week, while Jamie saves $3 a week. If Alex starts with $20 and Jamie starts with $10, how many weeks will it take for them to have the same amount of money? Solve and graph the equations to find the answer.

• 3 weeks

• 10 weeks

• 7 weeks

• 5 weeks

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer drives 100 miles, how much will they pay? Write the equation and graph it to show the relationship between miles driven and total cost.

• $60

• $80

• $70

• $90

A farmer has two types of crops: corn and wheat. He can plant a total of 100 acres. Corn requires 2 acres per unit, and wheat requires 1 acre per unit. If he wants to maximize his production, how many units of each crop should he plant? Set up the equations and graph them to find the solution.

• 50 units of corn and 25 units of wheat.

• 75 units of corn and 25 units of wheat.

• 100 units of corn and 0 units of wheat.

• 100 units of wheat and 0 units of corn.

A gym offers two membership plans. Plan A costs $30 per month, and Plan B costs $20 per month plus a one-time fee of $100. After how many months will both plans cost the same? Write the equations and graph them to find the intersection point.

• 15 months

• 12 months

• 10 months

• 5 months

A bookstore sells novels for $12 each and textbooks for $25 each. If a customer buys a total of 10 books and spends $200, how many novels and textbooks did they buy? Create the equations and graph them to determine the quantities.

• 6 novels and 4 textbooks

• 4 novels and 6 textbooks

• 3 novels and 7 textbooks

• 5 novels and 5 textbooks

A pizza shop sells small pizzas for $8 and large pizzas for $12. If a customer orders a total of 5 pizzas and spends $52, how many of each size did they order? Formulate the equations and graph them to find the solution.

• 3 small pizzas and 2 large pizzas

• 2 small pizzas and 3 large pizzas

• 1 small pizza and 4 large pizzas

• 5 small pizzas and 0 large pizzas

A concert hall has two types of tickets: regular tickets for $50 and VIP tickets for $100. If a total of 200 tickets are sold for $10,000, how many of each type were sold? Set up the equations and graph them to visualize the solution.

• 200 regular tickets and 0 VIP tickets

• 150 regular tickets and 50 VIP tickets

• 100 regular tickets and 100 VIP tickets

• 50 regular tickets and 150 VIP tickets

A charity event sells raffle tickets for $5 each and donations for $10 each. If they sold a total of 150 tickets and raised $1,000, how many raffle tickets and donations were made? Write the equations and graph them to find the answer.

• 120 raffle tickets and 30 donations

• 80 raffle tickets and 70 donations

• 90 raffle tickets and 60 donations

• 100 raffle tickets and 50 donations