Systems of Inequalities TOTD

A school club is planning a fundraiser selling cookies and brownies. Each cookie requires 10 minutes to prepare and 5 minutes to package. Each brownie requires 15 minutes to prepare and 3 minutes to package. The club has at most 300 minutes available for preparation and 120 minutes for packaging. Create a system of inequalities to represent this situation and find one possible combination of cookies and brownies they could make.

• 10 cookies and 5 brownies

• 15 cookies and 12 brownies

• 20 cookies and 10 brownies

• 15 cookies and 15 brownies

A factory manufactures two types of smartphones: standard and premium. Each standard phone requires 2 hours of assembly and 1 hour of testing. Each premium phone requires 3 hours of assembly and 2 hours of testing. The factory has at most 60 hours available for assembly and less than 35 hours for testing. Create a system of inequalities and find one possible combination of phones they could produce.

• 20 standard phones and 5 premium phones

• 15 standard phones and 10 premium phones

• 20 standard phones and 10 premium phones

• 5 standard phones and 20 premium phones

A venue is selling regular and VIP tickets for a concert. Regular tickets cost $25 and VIP tickets cost $50. The venue wants to make at least $2000 in revenue and needs to sell more than 30 tickets total. The venue can accommodate no more than 100 people. Which of the following combinations are possible combinations of ticket sales?

• 40 regular tickets and 20 VIP tickets

• 30 regular tickets and 40 VIP tickets

• 50 regular tickets and 10 VIP tickets

• 20 regular tickets and 15 VIP tickets

You are planning a party and want to buy at least 20 total drinks. Cans of soda cost $1 and bottles of juice cost $2 each. You have no more than $30 to spend. Which of the following systems of inequalities represents all possible combinations of soda and juice you could buy?

• x + y ≥ 20

  x + 2y ≤ 30

• x + y ≤ 20

  x + 2y ≥ 30

• x + y ≥ 20

  x + 2y ≥ 30

• x + y ≤ 20

  x + 2y ≤ 30

A school fundraiser is selling t-shirts and hoodies. They need to sell more than 50 items total to reach their goal. T-shirts cost $10 and hoodies cost $25. They want to make at least $800 in sales.
Write a system of linear inequalities to represent the situation. Graph the system and explain what combinations of t-shirts and hoodies would allow them to reach their goals.

• (42, 28)

• (25, 15)

• (54, 12)

• (38, 23)