Quadratic formula: weekly price-demand equation is q = ....

[Gretta99]

I have a word problem to do:

"The weekly price-demand equation for medium pepperoni pizzas at a fast-food restaurant is
q=8,000-400p where q is the number of pizzas sold weekly and p is the price of one medium pepperoni pizza (in dollars) find the demand and the revenue when the price is $8."

I got this part and got an answer of 38,400, but there was a follow up problem that I didn't get.

"Refer to previous problem. Find the price p hat will produce each of the following revenues. Round answers to two decimal places.
(A) 38,000 I think If someone helps me with this one I can do the others.

Here's what I've done so far. Revenue=p(q) (my math teacher told me that) and where q= 8,000-400p I plugged that in for q so I had like terms.

38,000=p(8,000-400p)
38,000=8,000p-400p^2
0= -400p^2+8,000p-38,000
a=-400 b=8,000 c=-38,000 (Quadratic Formula)
P=(-8,000+/- sq root (-8,000^2-4(-400)(-38,000)))/2(-400)
P=-(8,000+/- sq root (3200000))/-800
p=(-8,000+/- 800 sq root (5))/-800
P=-(sq root (5) -10) or P=sq root (5) +10

I'm not sure how to go from here and figure out what the price or the revenue is out of that. Did I do some math wrong or am I on the right track. I assumed that I needed to do the quadratic formula or factor because that's what this sections about, but I couldn't factor it.

Thanks so much.

 

[mmm4444bot]

Good Job - Now, Use a Calculator ...

"The weekly price-demand equation for medium pepperoni pizzas at a fast-food restaurant is q=8,000-400p ... find the demand [q] and the revenue when the price is $8."
I got this part and got an answer of 38,400 ... ? This is correct for revenue, but report final answer in terms of money: $38,400.

(Also, you did not report your answer for the demand)

Find the price p that will produce ... $38,000 ... Here's what I've done so far ...
Revenue=(p)(q) ... (Revenue equation; use this to double-check your answers for the price when you think you're done)
38,000=p(8,000-400p)
38,000=8,000p-400p^2 ? Do you notice all of the zeros? You can make your life easier by reducing these coefficients before using the quadratic formula.

Divide both sides of the equation by 100 to get: -4p^2 + 80p - 380 = 0

Some people prefer one additional step before settling on a, b, and c. They prefer not to have a negative leading coefficient, so they multiply both sides of the equation by -1 (this is a matter of personal preference):

4p^2 - 80P + 380 = 0

P=-(sq root (5) -10) or P=sq root (5) +10 ? These are the correct values for p, although I would write the first one as 10 - sqrt(5)

I'm not sure how to go from here and figure out what the price or the revenue is out of that ...

Hi Gretta:

Good job, so far. Thank you for showing your work; we don't see that kind of effort around here very much!

It sounds to me like you forgot the goal of this exercise. Why are you concerned about finding the revenue? They already gave you that figure.

The question asks you to find the price (p) when the revenue is $38,000; that is why you set up the revenue equation equal to 38000 to begin with.

You solved that equation for p, and now you've got two candidates: p = 10 + sqrt(5) or p = sqrt(5) - 10.

You need to realize that it's time to put these expressions for the price into a calculator, and round them off to dollars and cents.

Then, double-check your results by making sure that your rounded answers produce a revenue that rounds to $38,000.

Please let us know if you need more help with these problems, and keep up the good work!

Cheers,

~Mark