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#
