Inequalities Context

Write the linear inequality in standard form for this situation:

Ms. Johnson is ordering pizzas and breadsticks for a school party and has a budget of no more than $81.

An order of breadsticks costs $7 and a pizza costs $13.

• 7x + 13y < 81

• 7x + 13y ≥ 81

• 7x + 13y ≤ 81

• 7x + 13y > 81

Answer explanation

The total cost of pizzas (y) and breadsticks (x) must be less than or equal to the budget of $81. Thus, the inequality is 7x + 13y ≤ 81, representing the maximum spending allowed.

Write the linear inequality in standard form for this situation: The DHS math department can spend no more than $2700 on textbooks this year. The department needs to buy both Algebra text books, which cost $57 each, and Geometry textbooks, which cost $72 each.

• 57x + 72y ≥ 2700

• 57x + 72y > 2700

• 57x + 72y < 2700

• 57x + 72y ≤ 2700

Answer explanation

The department can spend no more than $2700, so the total cost of textbooks, represented by 57x + 72y, must be less than or equal to 2700. Thus, the correct inequality is 57x + 72y ≤ 2700.

Write the linear inequality in standard form for this situation: In order to raise money to attend upcoming competitions, the Math Pentathalon team is selling apple cider and hot chocolate. They hope to make at least $240 by selling hot chocolate for $1 a glass and hot apple cider for $2 a glass.

• x + 2y < 240

• x + 2y > 240

• x + 2y ≤ 240

• x + 2y ≥ 240

Answer explanation

The team wants to make at least $240, so the inequality must reflect that they need to earn $240 or more. With x as the number of hot chocolate glasses and y as the number of apple cider glasses, the correct inequality is x + 2y ≥ 240.

Solve the system of inequalities by graphing.

• 
• 
• 
• 

On a cross-country bicycle trip, participants ride about 75 miles per day. Approximately how many days, d, must they ride to travel at least 4,275 miles?

Choose the inequality that correctly represents the situation.

• 75d < 4275

• 75d > 4275

• 75d ≥ 4275

A student is buying hot chips and sodas from the corner store. She can choose any combination of chips and sodas, and she does not want to spend more than $20. If hot chips cost $2.50 each and sodas costs $1.75 each, which inequality represents all possible combinations of x hot chips and y sodas?

• 2.5x + 1.75y ≥ 20

• 2.5x + 1.75y ≤ 20

• 2.5x + 1.75y < 20

• 1.75x + 2.5y ≥ 20

The Shoemaker Movie Theater is selling tickets to a new movie. Adult tickets cost $12 and child tickets cost $7. The goal is to sell at least $1000 worth of tickets for the Shoemaker Theater.

• 12a + 7c < 1000

• 12a + 7c < 1000

• 12a + 7c > 1000

• 12a + 7c > 1000

Maggie’s parents are booking a band and a DJ for a sweet 16, and wants to keep the cost of entertainment under $1,200. A band can play for part of the time at an hourly rate of $150, and a DJ can play for the remaining time at an hourly rate of $79. Write an inequality to describe the possible combinations of x band time and y DJ time?

• 150x + 79y < 1200

• 79x + 150y ≥ 1200

• 150x + 79y ≤ 1200

• 79x + 150y ≤ 1200

Baseball fans can buy tickets for seats in the lower deck or upper deck of the stadium. Tickets for the lower deck cost $42 each. Ticket prices for the upper deck cost $31.50. Write an inequality that represents all possible combinations of x, the number of tickets for the lower deck, and y, the number of tickets for the upper deck, that someone can buy for no more than $800?

An Uber’s rates are $1.35 per mile plus an additional $2.50 base fee. You have a weekly budget represented by B(x). Which inequality can be used to represent the amount of money you can spend without going over your budget.

• B(x) ≤ 1.35x + 2.50

• B(x) ≥ 1.35x + 2.50

• B(x) < 1.35x + 2.50

• B(x) > 1.35x + 2.50