SOLUTION: R=p(200 - p), where p equal and less than 200. Find R when p = 100 Find p when R = 7500

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: R=p(200 - p), where p equal and less than 200. Find R when p = 100 Find p when R = 7500      Log On


   

Question 549037: R=p(200 - p), where p equal and less than 200.
Find R when p = 100
Find p when R = 7500
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
Find R when p = 100
Subsituting p=100 into R=p(200-p) we get:
R=100%28200-100%29
R=100%28100%29
R=10000



Find p when R = 7500
Substituting R=7500 into R=p(200-p) we get:
7500=p%28200-p%29
7500=200p-p%5E2
p%5E2-200p-7500=0
We can now use the quadratic formula which says
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
And substituting our values in we get:
p=%28200%2B-sqrt%28200%5E2-4%2A1%2A%28-7500%29%29%29%2F2%2A1
p=%28200%2B-sqrt%2840000%2B30000%29%29%2F2
p=%28200%2B-sqrt%2870000%29%29%2F2
p=%28200%2B-sqrt%284%2A17500%29%29%2F2
p=%28200%2B-sqrt%284%29%2Asqrt%2817500%29%29%2F2
p=%28200%2B-2%2Asqrt%2817500%29%29%2F2
p=%282%28100%2B-sqrt%2817500%29%29%29%2F2
p=%28100%2B-sqrt%2817500%29%29