Equations, Inequalities, and Systems

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

The gardening club at school is growing vegetables. The club has 300 square feet of planting beds. Cucumber plants require 6 square feet of growing space, and tomato plants require 4 square feet of growing space. The students want to plant some of each type of plant and have at least 60 plants. Select all the equations or inequalities that could describe this situation. Let c represent the number of cucumber plants and represent the number of tomato plants. (hint, there are 3)

• c > 0

• t < 0

• c + t = 300

Graph the solution to the inequality 4x + 5y < 20.

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A jewelry artist is selling necklaces at an art fair. It costs $135 to rent a booth at the fair. The cost of materials for each necklace is $4.50. The artist is selling the necklaces at $12 each.
The inequality 12n > 135 + 4.50n represents the situation in which the artist makes a profit.

Will the artist make a profit if she sells 15 necklaces?

• No. If she sells 15 necklaces, her income will be $180, and she must make more than $202.50, which is the cost of making 15 necklaces.

• Yes. If she sells 15 necklaces, her income will be $202.50, which is more than the cost of making 15 necklaces.

A jewelry artist is selling necklaces at an art fair. It costs $135 to rent a booth at the fair. The cost of materials for each necklace is $4.50. The artist is selling the necklaces at $12 each.
The inequality 12n > 135 + 4.50n represents the situation in which the artist makes a profit.

Which inequality would show the number of necklaces, n, the artist must sell to make a profit. 

• n >14

• n >16

• n >18

How many solutions will this system have?

• One

• Two

• No Solution

• Infinitely Many Solutions

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

Solve this system of equations by graphing.

y = 1/2x + 2

y = -3x + 9

• (2, 3)

• (-2, -3)

• (3, 2)

• (-3, 2)

Solve the following system by graphing.  What is the solution?

• Infinite number of solutions

• (3, 3)

• (3, -3)

• (-3, 3)

What is the solution to the system of equations?

• (¹/₄, -¹³/₄)

• (¹/₄, -³/₄)

• (4,-22)

• (4,8)