Exploring Graph Intersections: Systems of Equations Quiz

1. 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. What are the possible dimensions of the pen?

• x = 30, y = 40

• The possible dimensions of the pen are x (length) and y (width) such that 0 < x < 50 and y = 50 - x.

• x = 60, y = 20

• x = 50, y = 0

2. Two friends, Alice and Bob, are selling lemonade and cookies. Alice sells lemonade for $2 per cup and Bob sells cookies for $1 each. If they both make $20, write a system of equations to represent their sales. How many cups of lemonade and cookies did they sell?

• Alice sold 8 cups of lemonade and Bob sold 25 cookies.

• Alice sold 5 cups of lemonade and Bob sold 15 cookies.

• Alice sold 12 cups of lemonade and Bob sold 8 cookies.

• Alice sold 10 cups of lemonade and Bob sold 20 cookies.

3. A school is planning a field trip. The cost of the bus is $300, and each student pays $15. Write a system of equations to find out how many students need to attend for the trip to be affordable. What is the intersection point of the equations?

• 20

• 30

• 25

• 15

4. A local gym charges a monthly fee of $30 plus $5 per class attended. Another gym charges a flat fee of $50 for unlimited classes. Write a system of equations to represent the total cost for each gym. At what point do the costs equal each other?

• 4 classes

• 10 classes

• 2 classes

• 6 classes

5. A concert hall has two types of tickets: regular tickets for $50 and VIP tickets for $100. If the total revenue from ticket sales is $5000, write a system of equations to find out how many of each type of ticket were sold. What does the intersection of the equations represent?

• The system of equations is: 50x + 100y = 5000 and x + y = total tickets sold.

• 100x + 50y = 5000 and x + y = 200

• 50x + 100y = 10000 and x + y = 100

• 50x + 100y = 5000 and x - y = total tickets sold

6. A car rental company charges a flat fee of $40 plus $0.20 per mile driven. Another company charges $30 plus $0.25 per mile. Write a system of equations to represent the total cost for each company. Where do the two lines intersect?

• The two lines intersect at (40, 48).

• The two lines intersect at (50, 40).

• The two lines intersect at (20, 80).

• The two lines intersect at (30, 60).

8. A pizza shop sells small pizzas for $8 and large pizzas for $12. If the total sales are $240, write a system of equations to represent the sales. How can you interpret the intersection of the equations?

• The system of equations is: 8x + 12y = 240 and x + y = total number of pizzas.

• 10x + 12y = 240 and x + 2y = total number of pizzas.

• 8x + 12y = 200 and x + y = total number of pizzas.

• 8x + 10y = 240 and x - y = total number of pizzas.

10. A company produces two products, A and B. Product A costs $10 to make and product B costs $15. If the total production cost is $300, write a system of equations to represent the production. What does the intersection point represent in this context?

• 10x + 20y = 300

• 15x + 10y = 300

• 5x + 10y = 300

• 10x + 15y = 300