Graphing Real-World Problems: Finding Intersection Points

1. A 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.

• 5 cupcakes and 10 cookies

• 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.

2. A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Another company charges $25 plus $0.25 per mile. Graph the cost equations and determine at what mileage the costs are the same.

• 120 miles

• 75 miles

• 100 miles

• 50 miles

3. A school is planning a field trip. The cost per student is $15 for a bus that holds 30 students and $10 for a bus that holds 50 students. Write the equations for the total cost and graph them to find the number of students where costs are equal.

• The costs are equal at 50 students.

• The costs are equal at 0 students.

• The costs are equal at 30 students.

• The costs are equal at 15 students.

4. Two friends are selling lemonade and cookies. Friend A sells lemonade for $3 per cup and cookies for $2 each, while Friend B sells lemonade for $2 per cup and cookies for $3 each. Graph their revenue equations and find the point where their revenues are equal.

• The revenues are equal when x + y = 5.

• The revenues are equal when x = y + 1.

• The revenues are equal when x = 2y.

• The revenues are equal when x = y.

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. Graph the equations and find the number of classes where both gyms cost the same.

• 1

• 3

• 5

• 2

6. A farmer has a total of 100 acres to plant corn and wheat. Corn requires 2 acres per unit and wheat requires 1 acre per unit. Write the equations for the area used and graph them to find the maximum number of units of corn and wheat that can be planted.

• 10 units of corn and 90 units of wheat

• 30 units of corn and 40 units of wheat

• 20 units of corn and 80 units of wheat

• The maximum number of units of corn and wheat that can be planted is 50 units of corn and 0 units of wheat, or 0 units of corn and 100 units of wheat.

7. A concert venue has two pricing models. One charges $50 per ticket with a maximum of 200 tickets, while another charges $40 per ticket with no limit. Graph the revenue equations and find the point where both venues earn the same revenue.

• Both venues earn the same revenue when 100 tickets are sold at the first venue and 200 tickets at the second venue.

• Both venues earn the same revenue when 150 tickets are sold at the first venue and 300 tickets at the second venue.

• Both venues earn the same revenue when 250 tickets are sold at the first venue and 400 tickets at the second venue.

• Both venues earn the same revenue when 200 tickets are sold at the first venue and 250 tickets at the second venue.

8. A store sells shirts for $20 each and pants for $30 each. If a customer has $200 to spend, write the equations for the total cost and graph them to find the combinations of shirts and pants they can buy.

• The total cost is $250 for 5 shirts and 5 pants.

• The equation is 10x + 20y = 200.

• The customer can only buy 10 shirts.

• The combinations of shirts and pants can be found by solving the equation 20x + 30y = 200 for non-negative integers x and y.

9. A delivery service charges a base fee of $10 plus $2 per mile. Another service charges a flat fee of $15 with no mileage fee. Graph the cost equations and determine the distance at which both services cost the same.

• 2.5 miles

• 5 miles

• 1 mile

• 3 miles

10. A school is selling tickets for a play. Adult tickets are $10 and student tickets are $5. If they sell a total of 100 tickets for $800, graph the equations and find the number of adult and student tickets sold.

• 60 adult tickets and 40 student tickets were sold.

• 70 adult tickets and 30 student tickets were sold.

• 80 adult tickets and 20 student tickets were sold.

• 50 adult tickets and 50 student tickets were sold.