Finding Intersections: Graphing Real-World Equations

A local bakery sells cupcakes and cookies. The cost of cupcakes is $2 each and cookies are $1 each. If a customer buys a total of 10 items for $18, how many cupcakes and cookies did they buy? Graph the equations and identify the intersection point.

• 6 cupcakes and 4 cookies

• 8 cupcakes and 2 cookies

• 7 cupcakes and 3 cookies

• 5 cupcakes and 5 cookies

Two friends are saving money to buy a video game. Friend A saves $3 a week, while Friend B saves $5 a week. If Friend A starts with $10 and Friend B starts with $20, how many weeks will it take for them to have the same amount saved? Graph the equations and identify the intersection point.

• 7 weeks

• 5 weeks

• 10 weeks

• 3 weeks

A farmer has two types of crops: corn and wheat. He can plant a total of 100 acres. Corn requires 2 acres per unit and wheat requires 1 acre per unit. If he wants to plant at least 40 units of corn, how many units of each crop can he plant? Graph the equations and find the intersection point.

• 20 units of corn and 60 units of wheat

• 40 units of corn and 20 units of wheat

• 50 units of corn and 0 units of wheat

• 30 units of corn and 40 units of wheat

A concert hall sells tickets for $15 for adults and $10 for children. If they sold a total of 200 tickets for $2,000, how many adult and child tickets were sold? Graph the equations and identify the intersection point.

• 200 adult tickets and 0 child tickets were sold.

• 0 adult tickets and 200 child tickets were sold.

• 50 adult tickets and 150 child tickets were sold.

• 100 adult tickets and 100 child tickets were sold.

A gym offers two membership plans. Plan A costs $30 per month and Plan B costs $20 per month plus a $50 initiation fee. If a member wants to spend no more than $200, how many months can they stay on each plan? Graph the equations and find the intersection point.

• Plan A: 4 months, Plan B: 8 months.

• Plan A: 7 months, Plan B: 5 months.

• Plan A: 6 months, Plan B: 7 months.

• Plan A: 5 months, Plan B: 6 months.

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Another company charges $30 plus $0.25 per mile. If a customer wants to spend no more than $100, how many miles can they drive with each company? Graph the equations and identify the intersection point.

• First company: 150 miles, Second company: 250 miles, Intersection at 70 miles.

• First company: 200 miles, Second company: 300 miles, Intersection at 90 miles.

• First company: 250 miles, Second company: 280 miles, Intersection at 80 miles.

• First company: 300 miles, Second company: 350 miles, Intersection at 100 miles.

A bookstore sells novels for $12 each and magazines for $5 each. If a customer buys a total of 15 items for $120, how many novels and magazines did they buy? Graph the equations and find the intersection point.

• 6 novels and 9 magazines

• 5 novels and 10 magazines

• 7 novels and 8 magazines

• 4 novels and 11 magazines

A charity is selling two types of gift baskets. The first type costs $25 and the second type costs $15. If they want to raise $500 and sell a total of 30 baskets, how many of each type did they sell? Graph the equations and identify the intersection point.

• 0 baskets of $25 type and 30 baskets of $15 type.

• 10 baskets of $25 type and 20 baskets of $15 type.

• 5 baskets of $25 type and 25 baskets of $15 type.

• 15 baskets of $25 type and 15 baskets of $15 type.

A pizza shop sells small pizzas for $8 and large pizzas for $12. If they sold a total of 50 pizzas for $480, how many small and large pizzas were sold? Graph the equations and find the intersection point.

• 15 small pizzas and 35 large pizzas

• 25 small pizzas and 25 large pizzas

• 30 small pizzas and 20 large pizzas

• 40 small pizzas and 10 large pizzas