A clothing designer uses $3 worth of fabric for each shirt she makes, and she sells each shirt for $15. She also spends $44 on supplies needed to make the shirts. How many shirts does she need to sell to earn a profit of $100

Step-by-step explanation:

We first need to figure out a game plan here. We know that what she earns when she sells a specific number of shirts - what she has to pay to make them = her profit.

If she makes $15 per shirt, and the number of shirts is what we are looking for, the expression that represents "what she earns when she sells a specific number of shirts" is 15x. x is the unknown number of shirts.

If she has to spend $3 per shirt, and again the number of shirts is what we are looking for, the expression that represents "what she has to pay to make them" is, in part, 3x. x is the unknown number of shirts. BUT she also has to add in the cost of the supplies at $44. So in its entirety, the expression for what she has to pay to make them is 3x - 44.

Her profit is $100 when she makes x amount of shirts.

The equation that represents her situaation is:

15x - (3x + 44) = 100 and

15x - 3x - 44 = 100 and

12x = 144 so

x = 12

She needs to make 12 shirts to earn $100 as a profit.