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 + color(red)(60) = s - 60 + color(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 * 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 * 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