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Solving and Graphing Inequalities in Two Variables

Authored by Anthony Clark

Mathematics

9th Grade

CCSS covered

Solving and Graphing Inequalities in Two Variables
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15 questions

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1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Lewis has 50-cent stamps and 23-cent stamps. He needs to use stamps totalling at least $3.70 to mail a package. There is enough room for up to 10 stamps on the package. This situation can be represented by the following system of inequalities, where x = number of 50-cent stamps and y = number of 23-cent stamps. x + y ≤ 10 50x + 23y ≥ 370 Which statement is true?

Lewis can use six 50-cent stamps and four 23-cent stamps.

Lewis can use five 50-cent stamps and five 23-cent stamps.

If Lewis uses six 50-cent stamps, he only needs to use two 23-cent stamp.

If Lewis uses fourteen 23-cent stamps, he only needs to use one 50-cent stamp.

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

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

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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)

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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.)

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per week. His goal is to make at least $300 per week.

Which system of equations or inequalities model the situation?

15x + 20y > 20

x + y        < 300

15x + 20y > 300

x + y     < 20

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

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