Xavier spent $84 on supplies (so this is an expense we will make only once), and then he will spend one more dollar for each canvas. So, his total expense for [tex]p[/tex] paintings will be
[tex]84+p[/tex]
Similarly, he will get 8 dollars for each painting, so he will earn
[tex]8p[/tex]
dollars if he will sell [tex]p[/tex] paintings.
In order to break even, earnings and costs must be equal:
[tex]84+p=8p[/tex]
Subtract p from both sides:
[tex]84=7p[/tex]
Divide both sides by 7:
[tex]12=p[/tex]
So, he has to sell at least 12 paintings to break even.
