To determine the break-even point of Amanda's store, we need to find the number of shirts [tex]\( n \)[/tex] at which her revenue equals her costs. The revenue function [tex]\( r \)[/tex] is given by [tex]\( r = 25n \)[/tex] and the cost function [tex]\( C \)[/tex] is given by [tex]\( C = 10n + 900 \)[/tex].
The break-even point occurs when revenue equals cost:
[tex]\[ 25n = 10n + 900 \][/tex]
To solve this equation for [tex]\( n \)[/tex], follow these steps:
1. Subtract [tex]\( 10n \)[/tex] from both sides to isolate [tex]\( n \)[/tex] on one side of the equation:
[tex]\[ 25n - 10n = 900 \][/tex]
2. Simplify the left side:
[tex]\[ 15n = 900 \][/tex]
3. Divide both sides of the equation by 15 to solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{900}{15} \][/tex]
4. Calculate the quotient:
[tex]\[ n = 60 \][/tex]
Thus, the break-even point is when Amanda sells 60 shirts.
So, the correct answer is:
C. [tex]\( n = 60 \)[/tex]
