8th Grade Challenge: Solve & Graph Systems of Equations

A farmer has 100 meters of fencing to create a rectangular pen for his sheep. If the length of the pen is represented by x and the width by y, write the equations for the perimeter and area. Graph the equations and find the dimensions that maximize the area.

• Length = 40 meters, Width = 10 meters

• Length = 50 meters, Width = 5 meters

• Length = 25 meters, Width = 25 meters

• Length = 30 meters, Width = 20 meters

A concert venue has two types of tickets: general admission for $30 and VIP tickets for $50. If the venue can hold 200 people and the total revenue from ticket sales is $8000, write a system of equations to represent the situation. Graph the equations and determine how many of each type of ticket were sold.

• 150 general admission tickets and 50 VIP tickets

• 100 general admission tickets and 100 VIP tickets

• 80 general admission tickets and 120 VIP tickets

• 200 general admission tickets and 0 VIP tickets

A local gym offers two membership plans. Plan A costs $20 per month and Plan B costs $15 per month plus a one-time fee of $50. If a customer wants to spend no more than $200, write a system of equations to represent the total cost. Graph the equations and find how many months each plan can be used within the budget.

• Plan A: 5 months, Plan B: 15 months

• Plan A: 8 months, Plan B: 12 months

• Plan A: 12 months, Plan B: 8 months

• Plan A: 10 months, Plan B: 10 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, write a system of equations to represent the situation. Graph the equations and determine how many novels and textbooks were purchased.

• 5 novels and 5 textbooks

• 6 novels and 4 textbooks

• 4 novels and 6 textbooks

• 3 novels and 7 textbooks

A pizza shop sells small pizzas for $8 and large pizzas for $12. If a customer orders a total of 15 pizzas and spends $120, write a system of equations to represent the order. Graph the equations and find out how many small and large pizzas were ordered.

• 0 small pizzas and 15 large pizzas

• 5 small pizzas and 10 large pizzas

• 15 small pizzas and 0 large pizzas

• 10 small pizzas and 5 large pizzas

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer has a budget of $100, write a system of equations to represent the total cost. Graph the equations and determine the maximum number of miles the customer can drive within the budget.

• 250 miles

• 150 miles

• 300 miles

• 200 miles

A charity event sells tickets for $10 each and donations of $5 each. If they want to raise at least $500, write a system of equations to represent the ticket sales and donations. Graph the equations and find the combinations of tickets and donations that meet the goal.

• (20, 50)

• (10, 60)

• (30, 40)

• The combinations of tickets and donations that meet the goal can be found by solving the inequality for various values of x, such as (50, 0), (45, 10), (40, 20), etc.

A bakery sells muffins for $3 each and cupcakes for $2 each. If they want to sell a total of 50 items and make at least $120, write a system of equations to represent the sales. Graph the equations and determine how many muffins and cupcakes they need to sell.

• 30 muffins and 20 cupcakes

• 40 muffins and 10 cupcakes

• 15 muffins and 35 cupcakes

• 25 muffins and 25 cupcakes