Linear Inequalities in Two Variables in Context

Is (0, 0) a solution to this inequality?

• Yes

• No

Yumi is determining the seating arrangement for her big dinner party.  Circular tables will seat 8 guests and rectangular tables can seat 10 guests.  Together, all of the tables must seat at least 162 guests.
Write an inequality that describes the situation.
Let x = # of circular tables
Let y = # of rectangular tables

• 8x + 10y < 162

• 8x + 10y > 162

• 8x + 10y ≤ 162

• 8x + 10y ≥ 162

Today we're going to look at systems of inequalities (more than one inequality graphed at the same time).
Do you think (2, -2) would be a solution to this system?

• Yes

• No

At the Big Bear video rental store, blank CDs cost $1.50 each and blank DVDs cost $3.25 each.  Which of the following statements best describes the number of CDs (c) and DVDs (d) that can be purchased for less than $65.00?

• 150c + 325d < 6,500

• 325c + 150d <6,500

• 150c + 325d ≤ 6,500

• 325c + 150d ≤ 6,500

A donut shop charges $0.70 for each donut and $0.30 for a carryout box.  Shirley has $5.00 to spend.  She needs to determine the most donuts (x) she can buy when she only puts them in one carryout box.  Which equation can be used to answer this problem?

• 70x + 30 < 500

• 30x + 70 < 500

• 70x + 30 ≤500

• 30x + 70 ≤ 500

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 this situation?

• 2x + 3y ≤ 18

• x + y ≤ 6

• x + y ≤ 9

• 3x + 2y ≤ 18

Write the linear inequality in standard form for this situation: A landscaping business is purchasing plants from a nursery to finish a project. It will cost $14 each to buy each tree and $5 each to buy each bush. The landscaper wishes to keep the spending under $1000.

• 14x + 5y ≥ 1000

• 14x + 5y < 1000

• 14x + 5y  ≤ 1000

• 14x + 5y > 1000

Solid or dashed line?  
Y ≥

• Solid

• Dashed

Grace has $45 at most in her purse.

• g<45

• g>45

• g≤45

• g≥45

My sister plans to sell more than 250 boxes of cookies.

• c>250

• c<250

• c≤250

• c≥250