Cost Price:
Roseanne's expenses include a one-time fee for the brushes ($4) and $87 for each painting.
If she were to create x paintings, the cost price will be:
[tex]C=87x+4[/tex]
Selling Price:
Each painting will be sold for $91. Therefore, the selling price for x paintings will be:
[tex]S=91x[/tex]
Breakeven Point:
Roseanne will break even when the cost and selling prices are equal. This means that:
[tex]87x+4=91x[/tex]
We can solve for x to be:
[tex]\begin{gathered} 91x-87x=4 \\ 4x=4 \\ \therefore \\ x=1 \end{gathered}[/tex]
This means that Roseanne will break even after selling 1 painting.
The cost will be:
[tex]\begin{gathered} C=87(1)+4=91 \\ C=91\text{ dollars} \end{gathered}[/tex]
The selling price will be:
[tex]\begin{gathered} C=91(1)=91 \\ C=91\text{ dollars} \end{gathered}[/tex]
ANSWER
Roseanne's expenses and receipts will both total $91 when she has sold 1 of her paintings.
