Writing Equations and Identifying Variables in Context

A school is selling tickets for a play. Adult tickets cost $10 each and student tickets cost $5 each. If the school sold a total of 50 tickets for $400, write a system of equations to represent the situation and identify the variables.

• x + y = 50, 15x + 5y = 400

• x + y = 50, 10x + 5y = 400

• x + y = 40, 10x + 5y = 300

• x + y = 60, 10x + 5y = 500

Maria and John are saving money for a concert. Maria saves $15 each week, while John saves $10 each week. If together they want to save $150 in total, write a system of equations to represent their savings and identify the variables.

• 15x + 10y = 100, x = y

• 20x + 5y = 150, x = y

• 15x + 10y = 200, x + y = 10

• 15x + 10y = 150, x = y

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 represent the number of chickens and cows, and identify the variables involved.

• x + y = 25, 2x + 4y = 90

• x + y = 35, 2x + 4y = 110

• x + y = 30, 2x + 3y = 100

• x + y = 30, 2x + 4y = 100

In a bookstore, the price of a novel is $12 and the price of a magazine is $5. If a customer buys a total of 20 items for $150, write a system of equations to represent the situation and identify the variables.

• x + y = 20, 15x + 5y = 180

• x + y = 20, 12x + 5y = 150

• x + y = 15, 10x + 5y = 120

• x + y = 25, 12x + 5y = 160

Two friends, Alex and Jamie, are collecting coins. Alex has twice as many coins as Jamie. Together, they have 36 coins. Write a system of equations to represent the number of coins each has and identify the variables.

• x + 3x = 36 and x = Jamie's coins, 3x = Alex's coins.

• The system of equations is: x + 2x = 36 and x = Jamie's coins, 2x = Alex's coins.

• x + y = 36 and y = Alex's coins, x = Jamie's coins.

• x + 2y = 36 and y = Jamie's coins, x = Alex's coins.

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer pays $70 for a rental, write a system of equations to represent the situation and identify the variables involved.

• C = 50 + 0.20x, C = 70

• C = 60 + 0.20x, C = 70

• C = 50 + 0.15x, C = 60

• C = 50 + 0.25x, C = 70

In a fruit market, apples cost $2 each and bananas cost $1 each. If a customer buys a total of 15 fruits for $25, write a system of equations to represent the situation and identify the variables.

• x + y = 15, 3x + y = 25

• x + y = 10, 2x + y = 20

• x + y = 15, 2x + y = 25

• x + y = 20, 2x + y = 30

A gym offers two types of memberships: a monthly membership for $30 and a yearly membership for $300. If a customer spends a total of $360 on memberships, write a system of equations to represent the situation and identify the variables.

• 30x + 300y = 360, x + y = total memberships.

• 15x + 150y = 360, x + y = total memberships.

• 30x + 300y = 360, x - y = total memberships.

• 30x + 300y = 600, x + y = total memberships.

A school is organizing a field trip. The cost of a bus is $200 and each student pays $10. If 30 students are going, write a system of equations to represent the total cost and identify the variables involved.

• x = 200 + 10y; y = 25

• x = 200 + 10y; y = 30

• x = 200 - 10y; y = 30

• x = 150 + 10y; y = 30

In a bakery, a cake costs $15 and a pie costs $10. If a customer buys a total of 8 items for $100, write a system of equations to represent the situation and identify the variables.

• x + y = 8, 15x + 10y = 100

• x + y = 10, 15x + 5y = 100

• x + y = 5, 15x + 10y = 80

• x + y = 8, 20x + 10y = 100