If A is partly constant and partly varies as P. When A=15 and P =21 and when A=21,P =24. Find the law of variation between A and P
To find the law of variation between A and P, we need to determine the constant part and the varying part of A in terms of P.
Let's denote the constant part of A as C and the varying part as V. Therefore, we have:
A = C + V
We know that A = 15 when P = 21. Substituting these values into the equation, we get:
15 = C + V
We also know that A = 21 when P = 24. Substituting these values into the equation, we get:
21 = C + V
We now have a system of two equations:
15 = C + V
21 = C + V
By subtracting the first equation from the second equation, we eliminate the constant part (C) and obtain:
21 - 15 = (C + V) - (C + V)
6 = 0
This implies that there is no constant part (C) in the variation between A and P. Therefore, A varies directly with P.
The law of variation between A and P can be written as:
A = kP
where k is the constant of variation.