Matilda is selling hand-painted vases at a craft fair. She will have to pay $200 to rent a booth at the fair. The cost of the
paint and other materials to create each vase is $5.50. She is
going to sell each vase for $14.00.
Part 1. Write an inequality to represent the situation in which
Matilda makes a profit. You must define any variable(s) you
use.
Part 2. How many vases must Matilda sell to make a profit?
Explain your reasoning.

14v > 200 + 5.50v, she will have to sell 24 vases to make a profit

Step-by-step explanation:

It costs $5.50 PER VASE for materials, so you would subtract this from what she sells each vase for. 14 - 5.50 = 8.50. She makes an $8.50 profit per vase sold. We can write 8.50n > 200 to show her profit margin minus the booth fee. If she sold 24 vases, she would be making a profit and this would represent the lowest amount of vases she can sell to make a profit. We can write the inequality 24 ≤ n to show that she can sell 24 vases or more to make a profit.

14n > 200 + 5.50n

336 > 332, true

n > 23

Hope This Helps!