Mastering Systems of Equations: Identify & Write Equations

A school is planning a field trip. The cost for a bus is $200 and the cost for each student is $10. If the total cost for the trip is $500, how many students are going? Identify the variables and write the equations in standard form.

• 40

• 35

• 25

• 30

A farmer has chickens and cows. The total number of animals is 30, and the total number of legs is 100. Let x be the number of chickens and y be the number of cows. Write the system of equations in standard form.

• x + y = 25, 2x + 4y = 90

• x + y = 30, 2x + 4y - 100 = 0

• x + y = 35, 2x + 4y = 110

• x + y = 30, 2x + 4y = 100

A concert hall has two types of tickets: regular tickets for $50 and VIP tickets for $100. If 200 tickets were sold for a total of $10,000, how many of each type were sold? Identify the variables and write the equations in standard form.

• 150 regular tickets and 50 VIP tickets

• 100 regular tickets and 100 VIP tickets

• 0 regular tickets and 200 VIP tickets

• 200 regular tickets and 0 VIP tickets

A bookstore sells fiction and non-fiction books. The total number of books sold is 150, and the total revenue is $1,200. If fiction books cost $8 each and non-fiction books cost $12 each, write the system of equations in standard form.

• x + y = 150; 2x + 3y = 300

• x + y = 200; 2x + 3y = 400

• x + y = 100; 2x + 3y = 250

• x + y = 150; 2x + 3y = 150

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer paid $50 for a rental, how many miles did they drive? Identify the variables and write the equations in standard form.

• 100 miles

• 120 miles

• 50 miles

• 80 miles

A local gym offers two membership plans: a monthly plan for $40 and an annual plan for $400. If 100 memberships were sold for a total of $3,000, how many of each type were sold? Write the system of equations in standard form.

• x + y = 80; 40x + 400y = 2500

• x + y = 150; 40x + 400y = 4000

• x + y = 120; 40x + 400y = 3500

• x + y = 100; 40x + 400y = 3000

A bakery sells cupcakes and cookies. The total number of baked goods is 80, and the total revenue is $320. If cupcakes cost $4 each and cookies cost $2 each, identify the variables and write the equations in standard form.

• x + y = 100; 4x + 3y = 320

• x + y = 60; 3x + 2y = 240

• x + y = 80; 4x + 2y = 320

• x + y = 80; 5x + 2y = 400

A charity event sold tickets for $15 each and VIP tickets for $25 each. If they sold a total of 300 tickets for $5,000, how many of each type were sold? Write the system of equations in standard form.

• x + y = 300; 20x + 25y = 5000

• x + y = 250; 15x + 20y = 5000

• x + y = 300; 10x + 30y = 5000

• x + y = 300; 15x + 25y = 5000

A pet store has dogs and cats. The total number of pets is 50, and the total number of legs is 140. Let x be the number of dogs and y be the number of cats. Identify the variables and write the equations in standard form.

• x + y = 50; 4x + 2y = 140

• x + y = 50; 3x + 3y = 140

• x + y = 50; 2x + 4y = 140

• x + y = 50; 4x + 4y = 140

A company produces two types of gadgets. The total production is 120 gadgets, and the total cost is $1,800. If type A costs $15 each and type B costs $25 each, write the system of equations in standard form.

• x + y = 120; 20x + 25y = 1800

• x + y = 150; 10x + 30y = 1800

• x + y = 120; 15x + 25y = 1800

• x + y = 100; 15x + 20y = 1800