Solving and Graphing Linear Equations in Real-World Scenarios

1. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the equation for the total cost (C) in terms of miles driven (m). If another company charges $30 plus $0.25 per mile, write the equation for their total cost. How many miles must you drive for both companies to charge the same amount?

• 350 miles

• 600 miles

• 200 miles

• 400 miles

2. Sarah and Tom are selling lemonade. Sarah sells her lemonade for $2 per cup, while Tom sells his for $1.50 per cup. Write the equations for their total earnings (E) based on the number of cups sold (c). How many cups must each sell for their earnings to be equal?

• They must sell 1 cup for their earnings to be equal.

• They must sell 4 cups for their earnings to be equal.

• They must sell 2 cups for their earnings to be equal.

• They must sell 0 cups for their earnings to be equal.

3. A local gym offers a monthly membership for $40 plus $5 per class attended. Another gym charges $30 per month with no class fees. Write the equations for the total cost (C) for each gym. How many classes must you attend for both gyms to cost the same?

• 0 classes

• 5 classes

• 1 class

• 2 classes

4. A school is planning a field trip. The cost per student is $15 for the bus and $5 for admission. Another option is a $10 bus fee and $10 admission. Write the equations for the total cost (C) based on the number of students (s). How many students must attend for both options to cost the same?

• Both options are only equal when there are 5 students.

• Any number of students (both options cost the same for all s)

• At least 10 students must attend for both options to cost the same.

• The first option is cheaper for any number of students.

5. A phone company offers a plan for $30 a month plus $0.10 per text. Another company charges $20 a month with $0.15 per text. Write the equations for the total monthly cost (C) based on the number of texts (t). How many texts must you send for both plans to cost the same?

• 250

• 150

• 200

• 100

6. A bakery sells cupcakes for $3 each and cookies for $2 each. If you buy a total of 10 items and spend $24, write a system of equations to represent the situation. How many cupcakes and cookies did you buy?

• 4 cupcakes and 6 cookies

• 5 cupcakes and 5 cookies

• 3 cupcakes and 7 cookies

• 2 cupcakes and 8 cookies

7. A farmer sells apples for $1.50 per pound and oranges for $2 per pound. If he sells a total of 50 pounds of fruit for $90, write a system of equations to find out how many pounds of each fruit he sold.

• x + y = 40, 1.5x + 2y = 80

• x + y = 60, 1.5x + 2y = 100

• x + y = 50, 1.5x + 2y = 90

• x + y = 50, 1.5x + 2y = 70

8. A concert venue has two pricing options for tickets. The first option is $50 per ticket, and the second option is $40 plus a $10 service fee. Write the equations for the total cost (C) based on the number of tickets (t). How many tickets must you buy for both options to cost the same?

• 2

• 5

• 3

• 1

9. A bookstore sells novels for $12 each and textbooks for $25 each. If a customer buys a total of 8 books and spends $156, write a system of equations to determine how many novels and textbooks were purchased.

• x + y = 10, 12x + 25y = 150

• x + y = 7, 12x + 25y = 160

• x + y = 8, 12x + 20y = 156

• x + y = 8, 12x + 25y = 156

10. A taxi company charges a base fare of $3 plus $2 per mile. Another company charges a flat rate of $10 for any distance. Write the equations for the total fare (F) based on the number of miles (m). How many miles must you travel for both companies to charge the same fare?

• 3.5 miles

• 2 miles

• 5 miles

• 4 miles