To find the break-even point for Amanda's clothing store, we need to determine when her revenue equals her costs. The revenue function is given by [tex]\( r = 25n \)[/tex], and the cost function is given by [tex]\( C = 10n + 900 \)[/tex].
The break-even point is when the revenue equals the cost:
[tex]\[ 25n = 10n + 900 \][/tex]
We start by isolating the variable [tex]\( n \)[/tex]. To do this, we subtract [tex]\( 10n \)[/tex] from both sides of the equation:
[tex]\[ 25n - 10n = 900 \][/tex]
Simplifying the left side, we get:
[tex]\[ 15n = 900 \][/tex]
Next, we solve for [tex]\( n \)[/tex] by dividing both sides of the equation by 15:
[tex]\[ n = \frac{900}{15} \][/tex]
Using simple division,
[tex]\[ n = 60 \][/tex]
Thus, the break-even point is [tex]\( n = 60 \)[/tex]. So, Amanda needs to sell 60 shirts each month to break even.
Therefore, the correct answer is:
A. [tex]\( n = 60 \)[/tex]
