Question

An artist plans to sell $250 of prints online each week. This week, she is within $25 of her goal.

Part A: Define a variable and write an absolute value equation to represent the scenario. (4 points)

Part B: Solve the equation, showing all steps. (4 points)

Part C: What are the minimum and maximum amounts that the artist received for her products? (2 points)

Answer 1

Part A:
Let x be the amount the artist received for her products.
The absolute value equation that represents the scenario is |x - 250| = 25.

Part B:
We need to solve the absolute value equation |x - 250| = 25.

If x - 250 is positive, then |x - 250| = x - 250.
If x - 250 is negative, then |x - 250| = -(x - 250).

So, we need to solve two equations:
x - 250 = 25 and -(x - 250) = 25

Solving the first equation, we get:
x - 250 = 25
x = 275

Solving the second equation, we get:
-(x - 250) = 25
-x + 250 = 25
-x = -225
x = 225

Therefore, the solutions are x = 225 and x = 275.

Part C:
The minimum amount that the artist received for her products is $225, and the maximum amount is $275.

Answer 2

Part A:

Let x be the amount the artist receives for her products this week. Then, the absolute value equation that represents the scenario is:

|250 - x| ≤ 25

Part B:

To solve the equation, we need to consider two cases:

Case 1: 250 - x ≤ 25

In this case, we have:

250 - x ≤ 25

x ≤ -225

x ≥ 225

Case 2: 250 - x ≥ -25

In this case, we have:

250 - x ≥ -25

x ≥ -275

x ≤ 275

Therefore, the solution to the absolute value equation is:

225 ≤ x ≤ 275

Part C:

The minimum amount the artist received for her products is $225, and the maximum amount is $275.

Explanation: