Solving Real-World Problems: Graphing Equations for 8th Grade

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 find the dimensions if the area is maximized.

• Length: 30 meters, Width: 20 meters

• Length: 40 meters, Width: 10 meters

• Length: 25 meters, Width: 25 meters

• Length: 50 meters, Width: 5 meters

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 want to make a total of $50, write the equations and determine how many cups of lemonade and cookies they need to sell if they sell 10 cups of lemonade.

• Alex sells 10 cups of lemonade and Jamie sells 40 cookies.

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

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

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

A school is planning a field trip and has a budget of $300. The cost per student for the bus is $15 and for the entrance fee is $10. Write the system of equations to represent the total cost and find out how many students can attend if the total cost is exactly $300.

• 20

• 10

• 12

• 15

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 $1200 and the number of tickets sold is 40, write the equations and determine how many of each type of ticket were sold.

• 20 regular tickets and 20 VIP tickets

• 30 regular tickets and 10 VIP tickets

• 40 regular tickets and 0 VIP tickets

• 10 regular tickets and 30 VIP tickets

A local bakery sells muffins for $3 each and cupcakes for $2 each. If they sold a total of 100 items and made $240, write the system of equations and find out how many muffins and cupcakes were sold.

• 50 muffins and 50 cupcakes

• 30 muffins and 70 cupcakes

• 20 muffins and 80 cupcakes

• 40 muffins and 60 cupcakes

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer paid $70 for their rental, write the equation to represent the total cost and determine how many miles they drove.

• 200 miles

• 100 miles

• 150 miles

• 50 miles

In a school, the number of boys is twice the number of girls. If the total number of students is 60, write the equations and find out how many boys and girls are in the school.

• Boys: 50, Girls: 10

• Boys: 20, Girls: 40

• Boys: 40, Girls: 20

• Boys: 30, Girls: 30

A bookstore sells novels for $15 and textbooks for $25. If they sold a total of 30 books and made $600, write the system of equations and determine how many novels and textbooks were sold.

• 25 novels and 5 textbooks

• 15 novels and 15 textbooks

• 10 novels and 20 textbooks

• 20 novels and 10 textbooks

A gym offers two types of memberships: a monthly membership for $40 and a yearly membership for $400. If a total of 50 memberships were sold and the total revenue was $1600, write the equations and find out how many of each type of membership were sold.

• 10 monthly memberships and 40 yearly memberships were sold.

• 30 monthly memberships and 20 yearly memberships were sold.

• 25 monthly memberships and 25 yearly memberships were sold.

• 20 monthly memberships and 30 yearly memberships were sold.

A pizza shop sells small pizzas for $10 and large pizzas for $15. If they sold a total of 20 pizzas and made $250, write the system of equations and determine how many small and large pizzas were sold.

• 0 small pizzas and 20 large pizzas

• 10 small pizzas and 10 large pizzas

• 12 small pizzas and 8 large pizzas

• 5 small pizzas and 15 large pizzas