Graphing and Analyzing Systems of Equations in Real Life

A farmer has 100 meters of fencing to create a rectangular pen for his animals. 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: 50 meters, Width: 5 meters

• Length: 40 meters, Width: 10 meters

• Length: 30 meters, Width: 20 meters

• Length: 25 meters, Width: 25 meters

A school is planning a field trip and has a budget of $300. The cost per student is $15 for transportation and $10 for admission. Write a system of equations to represent the total cost. Graph the equations and determine how many students can attend within the budget.

• 12

• 15

• 20

• 10

Two friends, Alex and Jamie, are selling lemonade and cookies. Alex sells lemonade for $2 per cup and cookies for $1 each, while Jamie sells lemonade for $1.50 per cup and cookies for $1.50 each. Write a system of equations to represent their total sales. Graph the equations and analyze who makes more money at different sales levels.

• The system of equations is: A = 3x + 2y and J = 2x + y.

• The system of equations is: A = 2x + y and J = 1.5x + 1.5y.

• The system of equations is: A = 1.5x + 2y and J = 2x + 1.5y.

• The system of equations is: A = 2x + 1.5y and J = 1.5x + y.

A concert hall has a seating capacity of 500. Tickets for adults are $20 and for children are $10. Write a system of equations to represent the total revenue based on the number of adult and child tickets sold. Graph the equations and find the combination of tickets that maximizes revenue.

• Sell 400 adult tickets and 100 child tickets for maximum revenue of $8,000.

• Sell 0 adult tickets and 500 child tickets for maximum revenue of $5,000.

• Sell 250 adult tickets and 250 child tickets for maximum revenue of $7,500.

• Sell 500 adult tickets and 0 child tickets for maximum revenue of $10,000.

A local 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. Write a system of equations to compare the costs over time. Graph the equations and determine after how many months the plans cost the same.

• 5 months

• 8 months

• 12 months

• 10 months

A bookstore sells novels for $12 each and textbooks for $25 each. If a customer buys a total of 10 books for $200, write a system of equations to represent the situation. Graph the equations and find how many novels and textbooks were purchased.

• 4 novels and 6 textbooks

• 5 novels and 5 textbooks

• 3 novels and 7 textbooks

• 2 novels and 8 textbooks

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Another company charges $30 plus $0.25 per mile. Write a system of equations to compare the costs. Graph the equations and determine which company is cheaper for different mileages.

• Both companies charge the same for all mileages.

• The first company is cheaper for mileages less than 400 miles, and the second company is cheaper for mileages greater than 400 miles.

• The second company is cheaper for mileages less than 200 miles.

• The first company is cheaper for all mileages.

A pizza shop sells small pizzas for $8 and large pizzas for $12. If a customer orders a total of 5 pizzas for $52, write a system of equations to represent the situation. Graph the equations and find how many small and large pizzas were ordered.

• 4 small pizzas and 1 large pizza

• 1 small pizza and 4 large pizzas

• 2 small pizzas and 3 large pizzas

• 3 small pizzas and 2 large pizzas

A company produces two types of gadgets. Type A costs $10 to produce and Type B costs $15. If the company has a budget of $300 and wants to produce a total of 30 gadgets, write a system of equations to represent the situation. Graph the equations and find the number of each type of gadget that can be produced.

• 30 Type A gadgets and 0 Type B gadgets

• 15 Type A gadgets and 15 Type B gadgets

• 20 Type A gadgets and 10 Type B gadgets

• 10 Type A gadgets and 20 Type B gadgets