Question

Write a system of equations to describe the situation below serve using substitution and fill in the blanks

Answer 1

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:

`C=87x+4`

Selling Price:

Each painting will be sold for $91. Therefore, the selling price for x paintings will be:

`S=91x`

Breakeven Point:

Roseanne will break even when the cost and selling prices are equal. This means that:

`87x+4=91x`

We can solve for x to be:

`\begin{gathered} 91x-87x=4 \\ 4x=4 \\ \therefore \\ x=1 \end{gathered}`

This means that Roseanne will break even after selling 1 painting.

The cost will be:

`\begin{gathered} C=87(1)+4=91 \\ C=91\text{ dollars} \end{gathered}`

The selling price will be:

`\begin{gathered} C=91(1)=91 \\ C=91\text{ dollars} \end{gathered}`

ANSWER

Roseanne's expenses and receipts will both total $91 when she has sold 1 of her paintings.