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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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