Solving and Graphing 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 a system of equations to represent the perimeter. Solve for x and y.

• x + y = 100, y = 100 - x

• x + 2y = 100, y = 50 - x

• x + y = 50, y = 50 - x; Example: x = 20, y = 30.

• 2x + 2y = 100, y = x - 10

A school is planning a field trip and has a budget of $500. The cost per student is $20 for transportation and $15 for admission. Write a system of equations to represent the total cost and the number of students. Solve for the number of students that can attend.

• 12

• 10

• 14

• 18

Two friends, Alex and Jamie, are selling lemonade and cookies. Alex sells lemonade for $2 per cup and Jamie sells cookies for $1 each. If they make a total of $50, write a system of equations to represent their sales. Solve for the number of cups of lemonade and cookies sold.

• Alex sold 20 cups of lemonade and Jamie sold 10 cookies.

• Alex sold 10 cups of lemonade and Jamie sold 30 cookies.

• Alex sold 15 cups of lemonade and Jamie sold 20 cookies.

• Alex sold 25 cups of lemonade and Jamie sold 5 cookies.

A concert hall has two types of tickets: regular tickets for $30 and VIP tickets for $50. If the total revenue from ticket sales is $1,200 and 40 tickets were sold, write a system of equations to represent the situation. Solve for the number of each type of ticket sold.

• 10 regular tickets and 30 VIP tickets

• 20 regular tickets and 20 VIP tickets

• 40 regular tickets and 0 VIP tickets

• 30 regular tickets and 10 VIP tickets

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer pays $50, write a system of equations to represent the cost. Solve for the number of miles driven.

• 120 miles

• 100 miles

• 75 miles

• 50 miles

A local bakery sells muffins for $3 each and cupcakes for $2 each. If they sold a total of 80 items and made $180, write a system of equations to represent the sales. Solve for the number of muffins and cupcakes sold.

• 10 muffins and 70 cupcakes

• 20 muffins and 60 cupcakes

• 30 muffins and 50 cupcakes

• 25 muffins and 55 cupcakes

A gym offers two membership plans: a monthly plan for $40 and an annual plan for $400. If 60 memberships were sold and the total revenue was $2,800, write a system of equations to represent the memberships. Solve for the number of each type sold.

• 40 monthly memberships and 20 annual memberships

• 30 monthly memberships and 30 annual memberships

• 59 monthly memberships and 1 annual membership

• 50 monthly memberships and 10 annual memberships

A bookstore sells novels for $10 each and textbooks for $25 each. If they sold a total of 100 books and made $1,500, write a system of equations to represent the sales. Solve for the number of novels and textbooks sold.

• 80 novels and 20 textbooks

• 50 novels and 50 textbooks

• 60 novels and 40 textbooks

• 70 novels and 30 textbooks

A pizza shop sells small pizzas for $8 and large pizzas for $12. If they sold a total of 50 pizzas and made $520, write a system of equations to represent the sales. Solve for the number of small and large pizzas sold.

• 10 small pizzas and 40 large pizzas

• 20 small pizzas and 30 large pizzas

• 15 small pizzas and 35 large pizzas

• 25 small pizzas and 25 large pizzas

A charity event sold tickets for $15 each and VIP tickets for $25 each. If they sold a total of 200 tickets and raised $3,500, write a system of equations to represent the ticket sales. Solve for the number of regular and VIP tickets sold.

• Regular tickets sold: 100, VIP tickets sold: 100

• Regular tickets sold: 150, VIP tickets sold: 50

• Regular tickets sold: 200, VIP tickets sold: 0

• Regular tickets sold: 120, VIP tickets sold: 80