Real-Life Linear Equations: Translating & Interpreting Solutions

A farmer has 100 meters of fencing to create a rectangular pen for his sheep. If the length of the pen is represented by x and the width by y, write the equations for the perimeter and find the dimensions if the area is maximized.

• Length: 40 meters, Width: 10 meters

• Length: 25 meters, Width: 25 meters

• Length: 50 meters, Width: 5 meters

• Length: 30 meters, Width: 20 meters

Two friends, Alex and Jamie, are selling lemonade and cookies. Alex sells lemonade for $2 per cup and Jamie sells cookies for $1 each. If they want to make a total of $50, write the equations and determine how many cups of lemonade and cookies they need to sell if they sell 10 cups of lemonade.

• Alex sells 10 cups of lemonade and Jamie sells 30 cookies.

• Alex sells 5 cups of lemonade and Jamie sells 25 cookies.

• Alex sells 15 cups of lemonade and Jamie sells 20 cookies.

• Alex sells 10 cups of lemonade and Jamie sells 40 cookies.

A school is planning a field trip and has a budget of $300. The cost per student for the bus is $15 and for the entrance fee is $10. Write the equation for the total cost and find out how many students can attend if the total cost is exactly $300.

• 20

• 15

• 10

• 12

A concert hall has two types of tickets: regular tickets for $30 and VIP tickets for $50. If the total revenue from ticket sales is $1200 and the number of tickets sold is 40, write the system of equations and determine how many of each type of ticket was sold.

• 30 regular tickets and 10 VIP tickets

• 20 regular tickets and 20 VIP tickets

• 40 regular tickets and 0 VIP tickets

• 10 regular tickets and 30 VIP tickets

A company produces two types of gadgets. Type A costs $20 to produce and Type B costs $30. If the company has a budget of $600 and wants to produce a total of 30 gadgets, write the equations and find out how many of each type they can produce.

• 30 Type A gadgets and 0 Type B gadgets

• 15 Type A gadgets and 15 Type B gadgets

• 10 Type A gadgets and 20 Type B gadgets

• 20 Type A gadgets and 10 Type B gadgets

In a local bakery, the cost of making a cake is $15 and the cost of making cookies is $5. If the bakery has a budget of $150 and wants to make a total of 20 items, write the equations and determine how many cakes and cookies can be made.

• 8 cakes and 12 cookies

• 5 cakes and 15 cookies

• 10 cakes and 10 cookies

• 3 cakes and 17 cookies

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 the equation for the total cost and find out how many miles they can drive without exceeding their budget.

• 150 miles

• 300 miles

• 250 miles

• 200 miles

A bookstore sells novels for $12 each and textbooks for $25 each. If a customer spends $200 and buys a total of 10 books, write the system of equations and determine how many novels and textbooks were purchased.

• 5 novels and 5 textbooks

• 3 novels and 7 textbooks

• 6 novels and 4 textbooks

• 4 novels and 6 textbooks

A gym offers two types of memberships: a monthly membership for $40 and a yearly membership for $400. If a customer wants to spend exactly $480, write the equations and find out how many monthly and yearly memberships they can buy.

• (1 monthly, 9 yearly)

• (10 monthly, 1 yearly)

• (0 monthly, 1 yearly) and (12 monthly, 0 yearly)

• (5 monthly, 5 yearly)

A local charity is organizing a fundraiser. They sell tickets for $15 each and snacks for $5 each. If they want to raise $300 and sell a total of 30 items, write the equations and determine how many tickets and snacks they sold.

• 10 tickets and 20 snacks

• 20 tickets and 10 snacks

• 25 tickets and 5 snacks

• 15 tickets and 15 snacks