SOLUTION: A company name Tropical Pools figure that its monthly revenue in dollars on the sale of x number of above ground pools is given by R = 1500x – 3x2, where x is less than 25. What n

Algebra ->  Pythagorean-theorem -> SOLUTION: A company name Tropical Pools figure that its monthly revenue in dollars on the sale of x number of above ground pools is given by R = 1500x – 3x2, where x is less than 25. What n      Log On


   

Question 200346: A company name Tropical Pools figure that its monthly revenue in dollars on the sale of x number of above ground pools is given by R = 1500x – 3x2, where x is less than 25. What number of pools would they have to sell to generate revenue of $17,568?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Given: R=1500x–3x^2, wheresystem%28R=Revenue%2C+x=pools%29

If R = $17,568,
17568=1500x-3x%5E2

Isolate all figures to the left, equating to zero: (change signs)
3x%5E2-1500x%2B17568=0

Divide all figures by "3":
x%5E2-500x%2B5856=0

By Quadraric wheresystem%28a=1%2Cb=-500%2Cc=5856%29

Solving discriminant: b%5E2-4ac=-500%5E2-4%281%29%285856%29=250000-11424=250000-23424=red%28226576%29

Then,
x=%28-%28-500%29%2B-sqrt%28226576%29%29%2F%282%281%29%29=%28500%2B-476%29%2F2
x=%28500%2B476%29%2F2=976%2F2=488
Also, x=%28500-476%29%2F2=24%2F2=highlight%28red%2812%29%29, Answer (less than 25 pools)

Check,
R=1500%28x%29-3x%5E2
17568=1500%2812%29-3%2812%29%5E2
17568=18000-432
17568=17568

Thank you,
Jojo