Real-Life Systems of Equations: Reasonableness & Graphing

A school is selling tickets for a play. Adult tickets cost $10 and student tickets cost $5. If they sold a total of 50 tickets for $400, how many adult and student tickets were sold? Check your answer for reasonableness.

• 40 adult tickets and 10 student tickets were sold.

• 30 adult tickets and 20 student tickets were sold.

• 25 adult tickets and 25 student tickets were sold.

• 20 adult tickets and 30 student tickets were sold.

Two friends, Alex and Jamie, are saving money for a concert. Alex saves $15 a week, while Jamie saves $10 a week. If they want to save a total of $150 together, how many weeks will it take for both of them to reach their goal? Graph the equations to visualize their savings.

• 6 weeks

• 5 weeks

• 8 weeks

• 7 weeks

A farmer has chickens and cows. If there are 20 animals in total and they have 60 legs, how many chickens and cows does the farmer have? Solve the system of equations and check if your answer makes sense.

• 12 chickens and 8 cows

• 15 chickens and 5 cows

• 5 chickens and 15 cows

• 10 chickens and 10 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 10 items for $80, how many novels and magazines did they buy? Graph the equations to find the solution.

• 2 novels and 8 magazines

• 3 novels and 7 magazines

• 5 novels and 5 magazines

• 4 novels and 6 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? Solve the system of equations and check for reasonableness.

• 75 miles

• 50 miles

• 120 miles

• 100 miles

At a bakery, a dozen cookies costs $18 and a dozen muffins costs $24. If a customer buys a total of 5 dozen baked goods for $120, how many dozens of cookies and muffins did they buy? Graph the equations to find the solution.

• 2 dozen cookies and 3 dozen muffins

• 0 dozen cookies and 5 dozen muffins

• 3 dozen cookies and 2 dozen muffins

• 1 dozen cookies and 4 dozen muffins

A gym has two types of memberships: a monthly membership for $25 and a yearly membership for $250. If a total of 100 memberships were sold for $2,500, how many of each type were sold? Check your answer for reasonableness.

• 75 monthly memberships and 25 yearly memberships were sold.

• 0 monthly memberships and 100 yearly memberships were sold.

• 100 monthly memberships and 0 yearly memberships were sold.

• 50 monthly memberships and 50 yearly memberships were sold.

In a fruit market, apples cost $2 each and bananas cost $1 each. If a customer buys a total of 30 fruits for $50, how many apples and bananas did they buy? Graph the equations to visualize the solution.

• 20 apples and 10 bananas

• 15 apples and 15 bananas

• 25 apples and 5 bananas

• 10 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? Solve the system of equations and check for reasonableness.

• 180 regular seats and 20 VIP seats were sold.

• 150 regular seats and 50 VIP seats were sold.

• 100 regular seats and 100 VIP seats were sold.

• 160 regular seats and 40 VIP seats were sold.