Question

Miguel made $17.15 profit from selling 7 custom t-shirts through a website. Miguel knows the total profit he earns is proportional to the number of shirts he sells, and he wants to create an equation which models this relationship so that he can predict the total profit from selling any number of t-shirts.

Answer 1

Let:

`\begin{gathered} P(x)=\text{profit} \\ k=\text{price of each t-shirt} \\ x=\text{Number of t-shirts sold} \end{gathered}`

Miguel made $17.15 profit from selling 7 custom t-shirts, therefore:

`\begin{gathered} P(7)=17.15=k(7) \\ 17.15=7k \\ \text{Solving for k:} \\ k=(17.15)/(7)=2.45 \end{gathered}`

Therefore, the equation that models this relationship is:

`P(x)=2.45x`