Susan sold t-shirts at a festival. She made $6 for each t-shirt she sold. Her expenses were $30. If she made a profit of $84, how many t-shirts did she sell?

Question

(a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 6, 30, and 84. Let x represent the number of t-shirts.
(b) Solve the equation in part (a) to find the number of t-shirts.

Answer 1

(a) To find the number of t-shirts Susan sold, we can use the following equation:

Profit = Revenue - Expenses

Here, her profit is $84, her revenue from selling t-shirts is \( 6x \) (where \( x \) is the number of t-shirts sold), and her expenses are $30. Therefore, we can set up the equation as follows:

\[ 84 = 6x - 30 \]

(b) Now, we'll solve the equation \( 84 = 6x - 30 \).

1. Add 30 to both sides:

   \[ 84 + 30 = 6x \] \[ 114 = 6x \]

2. Divide both sides by 6:

   \[ x = \frac{114}{6} \] \[ x = 19 \]

So, Susan sold 19 t-shirts.