<PRE><B>Question 1188918</B>
x = number of hours of use.


cost = 9150 + 8 * x = c(x).


revenue = 38.5 * x = r(x).


profit = p(x) = r(x) - c(x)


she will break even when p(x) = 0.


that means she neither makes a profit nor takes a loss.


youe equation is:


p(x) = r(x) - c(x)


when p(x) = 0, the equation becomes:


0 = r(x) - c(x)


since r(x) = 38.5 * x and c(x) = 9150 + 8 * x, the equation becomes:


0 = 38.5 * x - (9150 + 8 * x


simplify by removing parentheses to get:


0 = 38.5 * x - 9150 - 8 * x


combine like terms to get:


0 = 30.5 * x - 9150


add 9150 to both sides of the equation to get:


9150 = 30.5 * x


divide both sides by 30.5 to get:


9150 / 30.5 = x


solve for x to get:


x = 300


she will need to work 300 hours to break even.


r(x) = 38.5 * 300 = 11,550
c(x) = 9150 + 8 * 300 = 11,550
p(x) = r(x) - c(x) = 0


if she works more than 300 hours, r(x) will be positive and she will make a profit.
if she works less than 300 hours, r(x) will be negative and she will take a loss.


break even is when you neither take a profit nor take a loss.


let me know if you have any questions.


theo


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