Solving Real-World Systems: Analyzing Solutions & Variables

A local bakery sells cupcakes and cookies. The total number of baked goods sold in a day is 150. If the number of cupcakes sold is twice the number of cookies, how many cupcakes and cookies were sold? Identify the dependent variable.

• 100 cupcakes and 50 cookies

• 60 cupcakes and 90 cookies

• 120 cupcakes and 30 cookies

• 80 cupcakes and 70 cookies

A school is planning a field trip. The cost per student is $20 for transportation and $15 for admission. If the total cost for 30 students is $1050, how many students can attend if the budget is increased to $1500? Analyze the system solutions to find the maximum number of students.

• 42

• 50

• 30

• 35

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Another company charges a flat fee of $30 plus $0.25 per mile. How many miles must you drive for the costs to be the same? Analyze the system solutions to determine the mileage.

• 300 miles

• 400 miles

• 500 miles

• 200 miles

A farmer has a total of 100 animals, consisting of chickens and cows. If there are 3 times as many chickens as cows, how many of each type of animal does the farmer have? Identify the dependent variable in this problem.

• 30 cows and 70 chickens.

• 10 cows and 90 chickens.

• 50 cows and 50 chickens.

• 25 cows and 75 chickens.

A movie theater sells adult tickets for $12 and child tickets for $8. If the total revenue from ticket sales is $480 and 50 tickets were sold, how many adult and child tickets were sold? Analyze the system solutions to find the number of each ticket sold.

• 25 adult tickets and 25 child tickets

• 10 adult tickets and 40 child tickets

• 15 adult tickets and 35 child tickets

• 20 adult tickets and 30 child tickets

A 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. After how many months will the total costs of both plans be equal? Identify the dependent variable in this scenario.

• 10 months

• 12 months

• 5 months

• 8 months

A bookstore sells novels for $15 each and textbooks for $25 each. If a customer buys a total of 10 books and spends $200, how many novels and textbooks did they buy? Analyze the system solutions to determine the quantities of each type of book.

• 6 novels and 4 textbooks

• 4 novels and 6 textbooks

• 3 novels and 7 textbooks

• 5 novels and 5 textbooks

A concert venue has two types of seating: general admission tickets for $50 and VIP tickets for $100. If the total number of tickets sold is 200 and the total revenue is $12,000, how many of each type of ticket were sold? Identify the dependent variable in this problem.

• 160 general admission tickets and 40 VIP tickets were sold.

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

• 180 general admission tickets and 20 VIP tickets were sold.

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

A charity event sells tickets for $10 each and donations are collected at $5 per person. If the total amount raised is $500 and 60 people attended, how many tickets were sold? Analyze the system solutions to find the number of tickets sold.

• 30

• 50

• 40

• 20