Question

Gregor wants to open a small business selling handmade quilts. His total costs are modeled by C(x)=12x+350
. His daily revenue is given by R(x)=20+27x
, where x represents the number of quilts sold. How many quilts does Gregor need to sell in order to break even?

Answer 1

To find the break-even point, we need to set the total costs equal to the total revenue. The formulas provided are:

- Total costs: \( C(x) = 12x + 350 \)
- Total revenue: \( R(x) = 20 + 27x \)

To break even, we set \( C(x) = R(x) \):

\[
12x + 350 = 20 + 27x
\]

Now, let's solve for \( x \):

1. Subtract \( 12x \) from both sides:

\[
350 = 20 + 15x
\]

2. Subtract \( 20 \) from both sides:

\[
330 = 15x
\]

3. Divide both sides by \( 15 \):

\[
x = \frac{330}{15} = 22
\]

Thus, Gregor needs to sell **22 quilts** to break even.