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Amanda owns a clothing store that sells graphic T-shirts. [tex]\( n \)[/tex] is the number of shirts she sells each month. The revenue function of her store is [tex]\( r = 25n \)[/tex]. The cost function of her store is [tex]\( C = 10n + 900 \)[/tex]. Using your calculator, what is the break-even point of Amanda's store?

A. [tex]\( n = 60 \)[/tex]
B. [tex]\( n = 50 \)[/tex]
C. [tex]\( n = 25 \)[/tex]
D. [tex]\( n = 10 \)[/tex]

Sagot :

GinnyAnswer
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]
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