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.
What are Maria's total c
]
P = 12n − (3.5n + 40)
to calculate her total profit, in dollars, when she sells n tote bags.
What are Maria's total c
]
Answers
Answered by
GPT-4o mini
To find Maria's total profit using the equation provided, we first need to simplify the equation:
\[
P = 12n - (3.5n + 40)
\]
Distributing the negative sign:
\[
P = 12n - 3.5n - 40
\]
Now, combine the like terms (\(12n\) and \(-3.5n\)):
\[
P = (12 - 3.5)n - 40
\]
Calculating \(12 - 3.5\):
\[
12 - 3.5 = 8.5
\]
Now substituting that back into the equation:
\[
P = 8.5n - 40
\]
This simplified equation represents Maria's total profit \(P\) in dollars when she sells \(n\) tote bags. The equation shows that:
- \(8.5n\) is the income she earns from selling \(n\) tote bags at $12 each, minus costs.
- The constant \(-40\) represents fixed costs.
Thus, Maria's total profit when she sells \(n\) tote bags is given by:
\[
P = 8.5n - 40
\]
\[
P = 12n - (3.5n + 40)
\]
Distributing the negative sign:
\[
P = 12n - 3.5n - 40
\]
Now, combine the like terms (\(12n\) and \(-3.5n\)):
\[
P = (12 - 3.5)n - 40
\]
Calculating \(12 - 3.5\):
\[
12 - 3.5 = 8.5
\]
Now substituting that back into the equation:
\[
P = 8.5n - 40
\]
This simplified equation represents Maria's total profit \(P\) in dollars when she sells \(n\) tote bags. The equation shows that:
- \(8.5n\) is the income she earns from selling \(n\) tote bags at $12 each, minus costs.
- The constant \(-40\) represents fixed costs.
Thus, Maria's total profit when she sells \(n\) tote bags is given by:
\[
P = 8.5n - 40
\]