Question #d4dfe

1 Answer
Jul 19, 2017

Answer:

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 + 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#