Graphing Linear Equations: Finding Intersections in Real Life

1. A local bakery sells cupcakes and cookies. The cost of cupcakes is $2 each and cookies are $1 each. If a customer spends $20, how many cupcakes and cookies could they buy? Graph the equations and find the intersection point.

• 15 cupcakes and 5 cookies

• 8 cupcakes and 12 cookies

• The customer can buy various combinations, such as 10 cupcakes and 0 cookies, or 0 cupcakes and 20 cookies.

• 5 cupcakes and 10 cookies

2. A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Another company charges $20 plus $0.25 per mile. How many miles would you need to drive for both companies to cost the same? Graph the equations and find the intersection point.

• 100 miles

• 250 miles

• 150 miles

• 200 miles

3. A school is planning a field trip. The cost per student for one option is $15, and for another option, it is $10 plus a $50 bus fee. If 100 students are going, how much will each option cost? Graph the equations and find the intersection point.

• Option 1 costs $1200 and Option 2 costs $950.

• Option 1 costs $2000 and Option 2 costs $1500.

• Option 1 costs $1500 and Option 2 costs $1050.

• Option 1 costs $1800 and Option 2 costs $1100.

4. Two friends are selling lemonade and cookies. One sells lemonade for $3 per cup and cookies for $2 each, while the other sells lemonade for $2 per cup and cookies for $3 each. If they both want to make $30, how many of each item do they need to sell? Graph the equations and find the intersection point.

• First friend: 6 cups of lemonade and 6 cookies; Second friend: 0 cups of lemonade and 10 cookies.

• 3 cups of lemonade and 12 cookies

• 5 cups of lemonade and 10 cookies

• 8 cups of lemonade and 4 cookies

5. A gym charges a monthly fee of $40 plus $5 per class attended. Another gym charges a flat fee of $50 with no additional class fees. How many classes would you need to attend for both gyms to cost the same? Graph the equations and find the intersection point.

• 1

• 3

• 2

• 4

6. A farmer has two types of crops: corn and wheat. He sells corn for $4 per bushel and wheat for $3 per bushel. If he wants to make $120, how many bushels of each crop does he need to sell? Graph the equations and find the intersection point.

• 50 bushels of corn and 10 bushels of wheat

• 20 bushels of corn and 20 bushels of wheat

• 10 bushels of corn and 30 bushels of wheat

• The farmer needs to sell 30 bushels of corn and 0 bushels of wheat, or 0 bushels of corn and 40 bushels of wheat.

7. A movie theater sells adult tickets for $12 and child tickets for $8. If they sold a total of 50 tickets for $480, how many adult and child tickets were sold? Graph the equations and find the intersection point.

• 15 adult tickets and 35 child tickets were sold.

• 25 adult tickets and 25 child tickets were sold.

• 10 adult tickets and 40 child tickets were sold.

• 20 adult tickets and 30 child tickets were sold.

8. A bookstore sells novels for $10 each and textbooks for $15 each. If a customer buys a total of 10 books for $120, how many novels and textbooks did they buy? Graph the equations and find the intersection point.

• 6 novels and 4 textbooks

• 4 novels and 6 textbooks

• 7 novels and 3 textbooks

• 5 novels and 5 textbooks

9. A pizza shop sells small pizzas for $8 and large pizzas for $12. If a customer orders a total of 5 pizzas for $52, how many small and large pizzas did they order? Graph the equations and find the intersection point.

• 2 small pizzas and 3 large pizzas

• 3 small pizzas and 2 large pizzas

• 0 small pizzas and 5 large pizzas

• 1 small pizza and 4 large pizzas

10. A clothing store sells shirts for $20 and pants for $30. If a customer spends $200 and buys a total of 8 items, how many shirts and pants did they buy? Graph the equations and find the intersection point.

• 5 shirts and 3 pants

• 2 shirts and 6 pants

• 4 shirts and 4 pants

• 6 shirts and 2 pants