SOLUTION: The monthly revenue of a mobile mechanic business is given by R = 420p - 3p2, where p is the hourly charge (in dollars) for the services the business provides. At what charge wi
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-> SOLUTION: The monthly revenue of a mobile mechanic business is given by R = 420p - 3p2, where p is the hourly charge (in dollars) for the services the business provides. At what charge wi
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Question 1162170: The monthly revenue of a mobile mechanic business is given by R = 420p - 3p2, where p is the hourly charge (in dollars) for the services the business provides. At what charge will the revenue be $12,000 if the price charged must be greater than $50? Provide your answer to the nearest dollar. Answer by Theo(13342) (Show Source):
if the revenue is 12,000, then the formula becomes:
12000 = 420 * p - 3 * p^2.
subtract 12000 from both sides of the equation and arrange the equation in descending order of degree and switch sides to get:
-3 * p^2 + 420 * p - 12000 = 0
divide both sides of the equation by 3 to get:
-p^2 + 140 * p - 4000 = 0
factor this quadratic equation to get:
( p - 40) * (p - 100) = 0
solve for p to get:
p = 40 or p = 100
since p must be greater than 50, then your solution is more then likely p = 100
replace p with 100 in the original equation to get:
R = 240 * 100 - 3 * 100^2 = 12000
your solution is that p must be equal to0 100 in order for the revenue to be equal to 12000.
the graph of the original equation looks like this:
y replaces R.
x replaces p.
