Solving Systems: Write Equations & Identify Variables

A school is selling tickets for a concert. Adult tickets cost $15 and student tickets cost $10. If the school sells a total of 200 tickets and makes $2,500, write a system of equations to represent the situation. Identify the variables.

• { x + y = 250, 15x + 10y = 3000 }

• { x + y = 150, 15x + 10y = 2000 }

• { x + y = 200, 20x + 5y = 2500 }

• The system of equations is: { x + y = 200, 15x + 10y = 2500 }

Maria has a total of 50 coins consisting of dimes and quarters. If the total value of the coins is $9.50, write a system of equations to represent the number of dimes and quarters. Identify the variables.

• d + q = 40; 0.10d + 0.25q = 8.50

• d + q = 50; 0.05d + 0.20q = 9.50

• d + q = 60; 0.10d + 0.25q = 10.00

• d + q = 50; 0.10d + 0.25q = 9.50

A farmer has chickens and cows. The total number of animals is 30, and the total number of legs is 100. Write a system of equations to find the number of chickens and cows. Identify the variables.

• x = 20 (chickens), y = 10 (cows)

• x = 10 (chickens), y = 20 (cows)

• x = 15 (chickens), y = 15 (cows)

• x = 25 (chickens), y = 5 (cows)

Two friends are saving money for a trip. Alex saves $50 a month, and Jamie saves $30 a month. If they want to save a total of $1,000 together, write a system of equations to represent their savings. Identify the variables.

• A = 50x, J = 20x, A + J = 800

• A = 40x, J = 30x, A + J = 1200

• A = 50x, J = 30x, A + J = 1000

• A = 50x, J = 30x, A + J = 900

A bookstore sells fiction and non-fiction books. The total number of books sold is 120, and the total revenue is $1,200. If fiction books cost $10 each and non-fiction books cost $15 each, write a system of equations to represent the situation. Identify the variables.

• x + y = 120, 10x + 20y = 1200

• x + y = 150, 5x + 10y = 1200

• x + y = 100, 10x + 15y = 1000

• x + y = 120, 10x + 15y = 1200

In a class, there are boys and girls. The total number of students is 40, and the total number of legs is 120. Write a system of equations to find the number of boys and girls. Identify the variables.

• There are 20 boys and 20 girls.

• 15 boys and 25 girls

• 30 boys and 10 girls

• 25 boys and 15 girls

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer pays $70 for a rental, write a system of equations to represent the situation. Identify the variables.

• C = 30 + 0.20x, C = 70

• C = 50 + 0.15x, C = 70

• C = 30 + 0.25x, C = 70

• C = 30 + 0.20x, C = 50

A local gym offers two types of memberships: a monthly membership for $25 and an annual membership for $250. If the gym has 100 members and makes $3,000 in membership fees, write a system of equations to represent the situation. Identify the variables.

• x + y = 200, 25x + 250y = 5000

• x + y = 100, 20x + 250y = 3000

• x + y = 50, 25x + 250y = 1500

• x + y = 100, 25x + 250y = 3000

A bakery sells muffins and cookies. The total number of baked goods sold is 150, and the total revenue is $450. If muffins cost $3 each and cookies cost $2 each, write a system of equations to represent the situation. Identify the variables.

• x + y = 150, 3x + 2y = 450

• x + y = 100, 3x + 2y = 300

• x + y = 200, 3x + 2y = 600

• x + y = 150, 4x + y = 450

A movie theater has two types of tickets: adult tickets for $12 and child tickets for $8. If the theater sells 200 tickets and makes $2,000, write a system of equations to represent the situation. Identify the variables.

• x + y = 150; 12x + 8y = 1800

• x + y = 200; 10x + 8y = 2000

• x + y = 250; 10x + 5y = 2000

• x + y = 200; 12x + 8y = 2000