Graphing Systems of Equations: Analyzing Solutions

A farmer has 100 meters of fencing to create a rectangular pen for his sheep. The length of the pen is 10 meters more than its width. Write a system of equations to represent the situation and graph the equations to find the dimensions of the pen.

• Width: 30 meters, Length: 40 meters

• Width: 25 meters, Length: 35 meters

• Width: 15 meters, Length: 25 meters

• Width: 20 meters, Length: 30 meters

A movie theater sells adult tickets for $12 and child tickets for $8. If they sold a total of 50 tickets and made $480, write a system of equations to represent the situation. Graph the equations to find how many adult and child tickets were sold.

• 10 adult tickets and 40 child tickets

• 20 adult tickets and 30 child tickets

• 25 adult tickets and 25 child tickets

• 15 adult tickets and 35 child tickets

A school is planning a field trip and has a budget of $300. The cost of a bus is $150 and each student pays $10. Write a system of equations to represent the situation and graph the equations to determine how many students can attend the trip within the budget.

• 10

• 15

• 20

• 25

A local gym offers two membership plans. Plan A costs $30 per month and Plan B costs $20 per month plus a one-time fee of $100. If a customer wants to spend no more than $300, write a system of equations to represent the situation and graph the equations to find out how many months they can afford each plan.

• A customer can afford up to 5 months for Plan A and 8 months for Plan B.

• A customer can afford up to 10 months for both Plan A and Plan B.

• A customer can afford up to 12 months for both Plan A and Plan B.

• A customer can afford only 6 months for Plan A and 4 months for Plan B.

A bookstore sells novels for $15 each and textbooks for $25 each. If a customer buys a total of 10 books and spends $200, write a system of equations to represent the situation. Graph the equations to find out how many novels and textbooks were purchased.

• 5 novels and 5 textbooks

• 4 novels and 6 textbooks

• 3 novels and 7 textbooks

• 6 novels and 4 textbooks

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer has a budget of $100, write a system of equations to represent the situation and graph the equations to find out how many miles they can drive without exceeding their budget.

• 300 miles

• 150 miles

• 100 miles

• 250 miles

Two types of fruit are being sold at a market: apples for $1 each and oranges for $2 each. If a customer buys a total of 30 fruits and spends $50, write a system of equations to represent the situation. Graph the equations to find out how many apples and oranges were purchased.

• 15 apples and 15 oranges

• 10 apples and 20 oranges

• 5 apples and 25 oranges

• 20 apples and 10 oranges

A concert venue has two types of tickets: general admission for $25 and VIP tickets for $50. If they sold a total of 200 tickets and made $7,500, write a system of equations to represent the situation. Graph the equations to find out how many general admission and VIP tickets were sold.

• 100 general admission tickets and 100 VIP tickets were sold.

• 200 VIP tickets were sold and no general admission tickets were sold.

• 75 general admission tickets and 125 VIP tickets were sold.

• 150 general admission tickets and 50 VIP tickets were sold.

A charity event is selling raffle tickets for $5 each and donations for $10 each. If they sold a total of 100 tickets and raised $600, write a system of equations to represent the situation. Graph the equations to find out how many raffle tickets and donations were made.

• 80 raffle tickets and 20 donations

• 90 raffle tickets and 10 donations

• 50 raffle tickets and 50 donations

• 70 raffle tickets and 30 donations