Question

An artist plans to sell $300 of prints online each week. This month, she is within $22 of her goal.

Part A: Define a variable and write an absolute value equation to represent the scenario.

Part B: Solve the equation, showing all steps.

Part C: What are the minimum and maximum amounts that the artist received for her products?

Answer 1

part a. to show your answer to the question, you will need to represent it.

Answer 2

Answer:

A)  |x - 1200| = 22

B)  x = 1222,  x = 1178

C)  Minimum = $1,178

    Maximum = $1,222

Step-by-step explanation:

Part A

Define the variable:

• Let x = revenue from prints sold this month.

Given information:

• The artist plans to sell $300 of prints each week.
• This month, she is within $22 of her goal.

If the artist plans to sell $300 of prints each week, then she plans to sell approx $1200 of prints each month, since there are approximately 4 weeks in each month.

If she is within $22 of her goal, this month then:

⇒ |x - 1200| = 22

Part B

To solve an equation containing an absolute value, set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation, then solve both equations:

Equation 1

⇒ x - 1200 = 22

⇒ x - 1200 + 1200 = 22 + 1200

⇒ x = 1222

Equation 2

⇒ x - 1200 = -22

⇒ x - 1200 + 1200 = -22 + 1200

⇒ x = 1178

Part C

Therefore:

• Minimum amount the artist received = $1,178
• Maximum amount the artist received = $1,222