Graphing & Solving Real-World Systems of Equations

A local bakery sells cupcakes and cookies. The total number of items sold is 50. If the number of cupcakes sold is twice the number of cookies, how many cupcakes and cookies were sold? Graph the equations to find the solution.

• Cupcakes: 40, Cookies: 10

• Cupcakes: 30, Cookies: 20

• Cupcakes: 50, Cookies: 0

• Cupcakes: 25, Cookies: 25

A school is organizing a field trip. The cost per student for the trip is $30, and the total cost for 40 students is $1200. If the school also has a fixed cost of $300 for the bus, write a system of equations to represent this situation and graph to find the number of students and total cost.

• The number of students is 20 and the total cost is $600.

• The number of students is 40 and the total cost is $1200.

• The number of students is 30 and the total cost is $900.

• The number of students is 35 and the total cost is $1050.

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $5 each week, while Jamie saves $10 each week. If they both start with $20, how many weeks will it take for them to have the same amount of money saved? Solve by graphing the equations.

• 3 weeks

• 2 weeks

• 1 week

• 0 weeks

A farmer has a total of 100 animals, consisting of chickens and cows. If there are 3 times as many chickens as cows, how many chickens and cows does the farmer have? Use a graph to find the solution.

• 30 cows and 70 chickens

• 50 cows and 50 chickens

• 25 cows and 75 chickens

• 20 cows and 80 chickens

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Another company charges a flat fee of $30 plus $0.25 per mile. How many miles would you need to drive for the costs to be the same? Graph the equations to find the answer.

• 200 miles

• 500 miles

• 400 miles

• 300 miles

In a school, the number of boys is represented by the equation B = 2G, where G is the number of girls. If the total number of students is 60, how many boys and girls are there? Solve this system by graphing.

• 50 boys and 10 girls

• 40 boys and 20 girls

• 30 boys and 30 girls

• 20 boys and 40 girls

A concert hall has two types of tickets: regular tickets for $20 and VIP tickets for $50. If the total revenue from ticket sales is $2000 and the number of tickets sold is 100, how many of each type of ticket were sold? Graph the equations to find the solution.

• 80 regular tickets and 20 VIP tickets

• 50 regular tickets and 50 VIP tickets

• 100 regular tickets and 0 VIP tickets

• 70 regular tickets and 30 VIP tickets

A bookstore sells novels and textbooks. The total number of books sold is 80, and the number of novels sold is 5 more than twice the number of textbooks. How many novels and textbooks were sold? Use a graph to find the answer.

• Novels: 50, Textbooks: 30

• Novels: 55, Textbooks: 25

• Novels: 60, Textbooks: 20

• Novels: 40, Textbooks: 40

A gym offers two membership plans. Plan A costs $30 per month, and Plan B costs $20 per month plus a one-time fee of $100. After how many months will the costs of both plans be equal? Graph the equations to find the solution.

• 8 months

• 12 months

• 5 months

• 10 months

A pizza shop sells two sizes of pizzas: small for $10 and large for $15. If the total number of pizzas sold is 40 and the total revenue is $500, how many small and large pizzas were sold? Solve this system by graphing.

• 25 small pizzas and 15 large pizzas

• 10 small pizzas and 30 large pizzas

• 20 small pizzas and 20 large pizzas

• 30 small pizzas and 10 large pizzas