Solving Systems of Equations: Context & Variables Challenge

A school is selling tickets for a play. Adult tickets cost $10 and student tickets cost $5. If they sold a total of 150 tickets for $1,200, how many adult and student tickets were sold? Identify the variables and constants in your equations.

• 80 adult tickets and 70 student tickets were sold.

• 100 adult tickets and 50 student tickets were sold.

• 60 adult tickets and 90 student tickets were sold.

• 90 adult tickets and 60 student tickets were sold.

Maria and John are saving money for a concert. Maria saves $15 each week, while John saves $10 each week. If they want to save a total of $300 together, how many weeks will it take for them to reach their goal? Interpret the solution in the context of their savings.

• 10 weeks

• 20 weeks

• 12 weeks

• 15 weeks

A farmer has chickens and cows. The total number of animals is 50, and the total number of legs is 140. How many chickens and cows does the farmer have? Define the variables and explain the solution in context.

• 15 chickens and 35 cows

• 40 chickens and 10 cows

• 25 chickens and 25 cows

• 30 chickens and 20 cows

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, how many novels and magazines did they buy? Identify the variables and constants in your equations.

• 10 novels and 10 magazines

• 7 novels and 13 magazines

• 8 novels and 12 magazines

• 5 novels and 15 magazines

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If a customer paid $50 for their rental, how many miles did they drive? Interpret the solution in the context of the rental agreement.

• 120 miles

• 50 miles

• 100 miles

• 75 miles

Two friends, Alex and Jamie, are collecting cans for recycling. Alex collects twice as many cans as Jamie. If together they collected 60 cans, how many cans did each collect? Identify the variables and explain the solution contextually.

• Alex collected 20 cans, Jamie collected 40 cans.

• Alex collected 30 cans, Jamie collected 30 cans.

• Alex collected 40 cans, Jamie collected 20 cans.

• Alex collected 50 cans, Jamie collected 10 cans.

A gym offers two types of memberships: a monthly membership for $25 and a yearly membership for $250. If a customer spends a total of $300 on memberships, how many of each type did they purchase? Define the variables and interpret the solution.

• 5 monthly memberships and 1 yearly membership

• 10 monthly memberships and 0 yearly memberships

• 6 monthly memberships and 0 yearly memberships

• 0 monthly memberships and 1 yearly membership

A bakery sells cupcakes for $3 each and cookies for $2 each. If they sold a total of 100 items for $240, how many cupcakes and cookies did they sell? Identify the variables and constants in your equations.

• 30 cupcakes and 70 cookies

• 50 cupcakes and 50 cookies

• 40 cupcakes and 60 cookies

• 20 cupcakes and 80 cookies

In a fruit market, apples cost $2 each and bananas cost $1 each. If a customer buys a total of 50 fruits for $80, how many apples and bananas did they buy? Explain the solution in the context of the market transaction.

• 40 apples and 10 bananas

• 10 apples and 40 bananas

• 25 apples and 25 bananas

• 30 apples and 20 bananas

A concert hall has two types of seating: regular seats for $50 and VIP seats for $100. If they sold a total of 200 seats for $12,000, how many regular and VIP seats were sold? Identify the variables and interpret the solution in context.

• 160 regular seats and 40 VIP seats were sold.

• 100 regular seats and 100 VIP seats were sold.

• 180 regular seats and 20 VIP seats were sold.

• 150 regular seats and 50 VIP seats were sold.