Framing/writing linear inequalities in two variables

I was told by my boss to buy pounds of hamburger meat for $6 each and packages of hotdogs for $4 each. I was told to spend at most $100. Which inequality matches my situation?

• 6x + 4y $<$ 100

• 6x + 4y $>$ 100

• 6x + 4y $\le$ 100

• 6x + 4y $\ge$ 100

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.
Which inequality represents the situation?

• x + y ≤ 8
• x + y ≤ 6
• 2x + 3y ≤ 6
• x + y ≤ 10

Tags

A2.ACE.3

Justin charges $11 to mow a small lawn and $26 to mow a large lawn. He would like to make at least $130.

Write an inequality that describes the situation.

Let x be the number of small lawns mowed and

y, the number of large lawns mowed.

• 11x + 26y ≥ 130

• 11x + 26y > 130

• 11x + 26y ≤ 130

• 11x + 26y < 130

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

The drama department has set a fundraising goal of at least $2,400 , which students will try to meet or exceed by selling two kinds of popcorn. There are profits of $3 for each container of caramel popcorn (x) and $1 for each container of chocolate-covered popcorn (y). Select the inequality that describes the situation. 

Se Chan is selling chocolate bars and orange juice in a carnival. Chocolate bars sell for RM2.50 each, and orange juice sell for RM3.50 each. The minimum of profit that Se Chan want is RM150, write an inequality showing the number of chocolate bars, b, and the number of orange juice, j, he must sell.

• 2.50b + 3.50j ≥ 150

• 2.50m + 3.50j > 150

• 2.50b + 3.50j ≤ 150

• 2.50m + 3.50j <150

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week. It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week.

Which inequality represents the total number of purses she can make?

• x + y ≤ 8

• x + y > 8

• 2x + 3y ≤ 18

• 2x + 3y >18

A store sells AirPods (a) and makes a $75 profit on the sale of each one. They also sell Apple Pencils (p) and they make $30 profit on those. The store wants to make a profit off these two items of at least $255. Which inequality describes this situation?

• $75a+30p<255$

• $75a+30p\le255$

• $75a+30p>255$

• $75a+30p\ge255$

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?

• A. 2.5x + 1.75y ≥ 20

• B. 2.5x + 1.75y ≤ 20

• C. 2.5x + 1.75y < 20

• D. 1.75x + 2.5y ≥ 20

Justin charges $11 to mow a small lawn and $26 to mow a large lawn. He would like to earn at least $130.

Write an inequality that describes the situation.

Let x = # of small lawns mowed and

Let y = # of large lawns mowed

• 11x + 26y ≥ 130

• 11x + 26y > 130

• 11x + 26y ≤ 130

• 11x + 26y < 130