Solving Real-World Systems: Graphing & Reasonableness Check

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 of each type of ticket did they sell? Check your answer for reasonableness.

• 30 adult tickets and 20 student tickets

• 40 adult tickets and 10 student tickets

• 20 adult tickets and 30 student tickets

• 25 adult tickets and 25 student tickets

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 them to reach their goal? Graph the equations to visualize their savings.

• 5 weeks

• 8 weeks

• 7 weeks

• 6 weeks

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

• 5 chickens and 15 cows

• 12 chickens and 8 cows

• 10 chickens and 10 cows

• 15 chickens and 5 cows

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Another company charges a flat fee of $20 plus $0.25 per mile. How many miles must you drive for both companies to charge the same amount? Graph the equations to find the solution.

• 200 miles

• 100 miles

• 250 miles

• 150 miles

In a fruit market, apples cost $2 each and bananas cost $1 each. If a customer buys a total of 10 fruits for $16, how many apples and bananas did they buy? Verify your solution by checking for reasonableness.

• 6 apples and 4 bananas

• 5 apples and 5 bananas

• 4 apples and 6 bananas

• 7 apples and 3 bananas

A bookstore sells novels for $12 and magazines for $5. If a customer buys a total of 8 items for $66, how many novels and magazines did they purchase? Solve the system and check if your answer is reasonable.

• 4 novels and 4 magazines

• 5 novels and 3 magazines

• 2 novels and 6 magazines

• 3 novels and 5 magazines

A local gym offers a monthly membership for $40 and a yearly membership for $400. If a person wants to find out how many months it would take for the yearly membership to be a better deal, set up the equations and solve. Graph the results to visualize the comparison.

• 12 months

• 10 months

• 9 months

• 11 months

In a school, the ratio of boys to girls is 3:2. If there are 50 students in total, how many boys and girls are there? Solve the system of equations and check if your answer is reasonable.

• 25 boys and 25 girls

• 40 boys and 10 girls

• 15 boys and 35 girls

• 30 boys and 20 girls

A pizza shop sells small pizzas for $8 and large pizzas for $12. If a customer buys a total of 5 pizzas for $52, how many small and large pizzas did they buy? Solve the equations and verify your solution for reasonableness.

• 1 small pizza and 4 large pizzas

• 2 small pizzas and 3 large pizzas

• 0 small pizzas and 5 large pizzas

• 3 small pizzas and 2 large pizzas

A concert hall has two types of seating: regular seats for $25 and VIP seats for $50. If a total of 100 seats were sold for $3500, how many of each type were sold? Solve the system and check your answer for reasonableness.

• 70 regular seats and 30 VIP seats were sold.

• 60 regular seats and 40 VIP seats were sold.

• 50 regular seats and 50 VIP seats were sold.

• 80 regular seats and 20 VIP seats were sold.