8th Grade Challenge: Graphing & Solving Linear Systems

1. A car rental company charges a flat fee of $20 plus $0.50 per mile driven. Write a system of equations to represent the total cost (C) for driving x miles. Graph the equations and find the point where the cost equals $50.

• 100 miles

• 80 miles

• 40 miles

• 60 miles

2. A local gym offers a membership for $30 per month plus $5 per class. Write a system of equations to represent the total cost (C) for attending y classes in a month. Solve the system to find how many classes can be attended for $100.

• 16

• 10

• 14

• 12

3. Two friends are selling lemonade. One sells it for $1.50 per cup and the other for $2.00 per cup. Write a system of equations to represent their total earnings (E) after selling x cups. Graph the equations and determine when their earnings are equal.

• Earnings are equal when x = 0 cups sold.

• Earnings are equal when x = 2 cups sold.

• Earnings are equal when x = 10 cups sold.

• Earnings are equal when x = 5 cups sold.

4. A phone plan charges a monthly fee of $25 plus $0.10 per text message. Write a system of equations to represent the total cost (C) for sending y messages. Solve the system to find the number of messages that can be sent for $50.

• 300

• 250

• 150

• 100

5. A school is planning a field trip. The cost per student is $15 for transportation and $10 for admission. Write a system of equations to represent the total cost (C) for x students. Graph the equations and find the total cost for 20 students.

• $600

• $400

• $300

• $500

6. A bakery sells cupcakes for $3 each and cookies for $2 each. Write a system of equations to represent the total sales (S) for x cupcakes and y cookies. Solve the system to find how many of each can be sold for $60.

• (5, 25)

• (15, 10)

• (30, 0)

• (0, 30), (10, 15), (20, 0)

7. A concert venue has two ticket pricing options: $50 for a regular ticket and $75 for a VIP ticket. Write a system of equations to represent the total revenue (R) from selling x regular and y VIP tickets. Graph the equations and find the revenue when 100 tickets are sold.

• R = 6000 when 100 tickets are sold.

• R = 7500 when 100 tickets are sold.

• R = 4500 when 100 tickets are sold.

• R = 5000 when 100 tickets are sold.

8. A farmer sells apples for $1.20 per pound and oranges for $0.80 per pound. Write a system of equations to represent the total income (I) from selling x pounds of apples and y pounds of oranges. Solve the system to find the total income for 50 pounds of fruit.

• $100

• 60

• $50

• $80

9. A bookstore sells novels for $10 each and magazines for $5 each. Write a system of equations to represent the total sales (S) for x novels and y magazines. Graph the equations and determine how many of each can be sold for $100.

• (12, -2)

• (2, 16)

• The combinations of novels (x) and magazines (y) that can be sold for $100 are: (0, 20), (5, 10), (10, 0) and any other combinations where 10x + 5y = 100.

• (8, 4)

10. A taxi company charges a base fare of $3 plus $2 per mile. Write a system of equations to represent the total fare (F) for traveling x miles. Solve the system to find the fare for a 10-mile trip.

• $23

• $15

• $30

• $18