# Question d4dfe

Jul 19, 2017

See a solution process below:

#### Explanation:

Profit is calculated by subtracting the cost of the product from the income the profit brought in:

$P = s - c$ Where:

$P$ is the profit of the enterprise. $48 for this problem. $s$is the sales of the products. What we need to solve for. $c$is the cost of the products.$60 for this problem.

Substituting and solving for $s$ gives:

$48 = s - 60$

$48 + \textcolor{red}{60} = s - 60 + \textcolor{red}{60}$

$108 = s - 0$

$108 = s$

$s = 108$

However, we need to know how much Camille is selling each doughnut for. The formula for this is:

$s = d \cdot n$

Where:

$s$ is the sales, from the solution above we know the sales where $108. $d$is the price of a doughnut, what we need to solve for. $n$is the number of doughnuts sold. The problem tells us Camille sold $80$doughnuts. Substituting and solving for $d$gives: $108 = d \cdot 80$$\frac{108}{\textcolor{red}{80}} = \frac{d \cdot 80}{\textcolor{red}{80}}$$1.35 = \frac{d \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{80}}}}{\cancel{\textcolor{red}{80}}}$$1.35 = d$$d = 1.5$In the original equation we can substitute $\mathrm{dn}$for $s$to give: $P = \mathrm{dn} - c$If we want a generic formula for Profit based on the number of donuts sold we can substitute: $1.35 for $d$ as this is the sales price per doughnut

$60# for $c$as the cost Camille paid for the doughnuts Giving: $P = 1.35 n - 60\$