Solving/Interpreting Linear Inequalities in Two Variables

The members of a new band want to spend no more than $75 for at least 60 fliers to advertise their upcoming concert.  The cost color fliers is $1.50 each, the cost of black and white fliers is $0.75 each. Which of the following combinations is a reasonable solution?

• 26 color, 30 black and white

• 30 color, 35 black and white

• 60 color

• 30 color, 50 black and white

Fatima likes her job as a baby-sitter, but it pays only $5 per hour. She has been offered a job as a tutor that pays $8 per hour. Her parents will allow her to work a maximum of 15 hours per week. Write a system of linear inequalities to determine many hours Fatima can baby-sit and tutor and make at least $100 per week.

• b + t < 15

  5b + 8t > 100

• b + t > 15

  5b + 8t < 100

• 5b + 8t > 15 b + t < 100

• 5b + 8t < 15 b + t < 100

Ms. Loredo is making her special cantaloupe-and-honeydew salad for a family gathering she is hosting and does not want to spend more than $30 at the supermarket. Currently, cantaloupes cost $3 each and honeydew melons cost $2 each. Which inequality in slope-intercept form best represents the number of cantaloupes, x, and honeydew melon, y. (Write an inequality first, then solve for y.)

A farmer has a field that can be used to grow two types of crops, corn and wheat. Each acre of corn requires 2 hours of labor and each acre of wheat requires 3 hours of labor. The farmer has a total of 40 hours of labor available. The farmer wants to grow at least 5 acres of corn and at least 8 acres of wheat. Write a system of linear inequalities to represent this situation.

• 2x + 3y >= 40, x <= 5, y <= 8.

• 2x + 3y <= 40, x <= 5, y <= 8.

• 2x + 3y >= 40, x >= 5, y <= 8.

• 2x + 3y <= 40, x >= 5, y >= 8

Write the system of inequalities:
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

• x+y≤300
  7.5x+5.5y≥2000

• x+y<300
  7.5x+5.5y≥2000

• x+y≤300
  7.5x+5.5y≤2000

• x+y>2000
  7.5x+5.5y≤300

Ximena and her children went into a restaurant and will buy hamburgers and tacos. Each hamburger costs $5.50 and each taco costs $4. Ximena has a total of $35 to spend on hamburgers and tacos.

Determine the maximum number of hamburgers purchased, h, and the number of tacos purchased, t that can be purchased without going over budget.

• h=5, t=5

• h=3, t=4

• h=6, t=2

• h=4, t=3

Solve each of the following systems of linear inequalities a graphing approach. Verify using a graphing calculator. Which of following are the vertices?

• (2, 0), (4, 5), (6, 0)

• (2, 0), (3, 5), (0, 6)

• (0, 2), (3.5, 4.5), (6, 2)

• (0, 0), (3, 5), (6, 0)

The girls’ swim team is hosting a fund raiser. They would like to raise at least $500. They are selling candles for $5 and flower arrangements for $6. The girls estimate that at most they will sell 200 items.

Which answer represents the system?