To determine how many purses Shirabi must sell to break even, we need to solve the equation representing her costs and revenues. The equation is given by:
[tex]\[ 208 + 10x = 36x \][/tex]
Where:
- 208 is the initial cost for the sewing machine.
- 10x represents the total variable cost for making [tex]\( x \)[/tex] purses, given that it costs \[tex]$10 to make each purse.
- 36x represents the total revenue from selling \( x \) purses at \$[/tex]36 each.
Our goal is to find [tex]\( x \)[/tex], the point at which her total costs equal her total revenues.
Let's solve the equation step-by-step:
1. Begin by simplifying the equation:
[tex]\[ 208 + 10x = 36x \][/tex]
2. Subtract [tex]\( 10x \)[/tex] from both sides to isolate the [tex]\( x \)[/tex] term on one side:
[tex]\[ 208 = 36x - 10x \][/tex]
3. Combine like terms on the right side:
[tex]\[ 208 = 26x \][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 26:
[tex]\[ x = \frac{208}{26} \][/tex]
5. Simplifying the fraction:
[tex]\[ x = 8 \][/tex]
Thus, Shirabi must sell 8 purses to break even.
The number of purses she must sell to break even is:
8
