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Answer 1 · 2017-07-19T17:12:08

See a solution process below:

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

$P = s - c$ $P = s - c$ Where:

$P$ $P$ is the profit of the enterprise. $48 for this problem.

$s$ $s$ is the sales of the products. What we need to solve for.

$c$ $c$ is the cost of the products. $60 for this problem.

Substituting and solving for $s$ $s$ gives:

$48 = s - 60$ $48 = s - 60$

$48 + 60 = s - 60 + 60$ $48 + color(red)(60) = s - 60 + color(red)(60)$

$108 = s - 0$ $108 = s - 0$

$108 = s$ $108 = s$

$s = 108$ $s = 108$

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

$s = d \cdot n$ $s = d * n$

Where:

$s$ $s$ is the sales, from the solution above we know the sales where $$ 108$ $$108$ .

$d$ $d$ is the price of a doughnut, what we need to solve for.

$n$ $n$ is the number of doughnuts sold. The problem tells us Camille sold $80$ $80$ doughnuts.

Substituting and solving for $d$ $d$ gives:

$108 = d \cdot 80$ $108 = d * 80$

$\frac{108}{80} = \frac{d \cdot 80}{80}$ $(108)/color(red)(80) = (d * 80)/color(red)(80)$

$1.35 = (d * color(red)(cancel(color(black)(80))))/cancel(color(red)(80))$

$1.35 = d$

$d = 1.5$

In the original equation we can substitute $dn$ for $s$ to give:

$P = dn - c$

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:

$P = 1.35n - 60$