Question

Maria paints custom tote bags and sells them at a community fair. She uses the equation
P = 12n - (3.5n + 40)
to calculate her total profit, in dollars, when she sells n tote bags.
Based on this equation, how much does she charge for each tote bag?
Profit, Revenue, Costs
$3.50
$8.50
$12.00
$40.00

Answer 1

To determine how much Maria charges for each tote bag, we can start by analyzing the equation she uses to calculate her total profit:

\[ P = 12n - (3.5n + 40) \]

In this equation:

- \( P \) represents total profit.
- \( 12n \) represents the total revenue from selling n tote bags at $12 each.
- \( (3.5n + 40) \) represents the total costs, where \( 3.5n \) is the variable cost per tote bag (with $3.50 being the cost to produce each bag) and $40 is a fixed cost.

To simplify the profit equation:

1. Distribute and combine like terms on the right side:
\[ P = 12n - 3.5n - 40 \]
\[ P = (12 - 3.5)n - 40 \]
\[ P = 8.5n - 40 \]

This shows that the profit depends on the number of tote bags sold, but we can see that the selling price per tote bag is $12 (from the revenue part of the equation).

Therefore, the answer is that Maria charges **$12.00** for each tote bag.