SOLUTION: <pre>How do you solve Pn A = ———————, for n? for P? for A? A - P</pre>

Algebra.Com
Question 31244: 
How do you solve

      Pn
A = ———————, for n? for P? for A?
     A - P
Answer by AnlytcPhil(1807)   (Show Source): You can put this solution on YOUR website!
How do you solve 

      Pn
A = ———————    ?
     A - P

You didn't give the complete instructions:

Solve it for what? 
Solve it for n?
Solve it for P?
Solve it for A?

You should always give the complete instructions.

If the instructions were "Solve for n":
      
      Pn
A = ———————
     A - P

Multiply both sides by (A - P)

A(A - P) = Pn

Divide both sides by P

 A(A - P)
—————————— = n
     P

     A(A - P)
n = —————————— 
         P

-------------------------

If the instructions were "Solve for P":
      
      Pn
A = ———————
     A - P

Multiply both sides by (A - P)

A(A - P) = Pn 

Aē - AP = Pn

Add AP to both sides

Aē = Pn + AP

Factor out P on the right

Aē = P(n + A)

Divide both sides by (n + A)

   Aē
———————  =  P
 n + A

       Aē
P = ———————  
     n + A


------------------------------

If the instructions were "Solve for A":
      
      Pn
A = ———————
     A - P

Multiply both sides by (A - P)

A(A - P) = Pn 

Aē - AP = Pn

Get 0 on the right by subtracting Pn from both sides

Aē - AP - Pn = 0

Use the quadratic formula with a = 1, b = -P, c = -Pn
                ________________
       -(-P) ą Ö(-P)ē- 4(1)(-Pn)    
A =  ——————————————————————————————
                  2(1)

            ________
       P ą ÖPē + 4Pn    
A =  ——————————————————
             2

or, you may factor out P under the radical but this isn't necessary:

            _________
       P ą ÖP(P + 4n)    
A =  ——————————————————
             2


Next time be sure to post the exact instructions.

Edwin
AnlytcPhil@aol.com
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