Relationships, direct, indirect

Question

If P is 12 when Q is 6, and if P varies indirectly as Q, what is Q when P is 8

Answer 1

When P varies inversely as Q, the equation is P = k * 1/Q where k is the constant of proportionality.

So we can re-write this equation as P = k/Q. Our first step is going to be to find k.

P= 12, Q =6 --> 12= k/6 . So we have to multiply 12 * 6 to find k. k = 72

Now that we know k, the equation can be re-written as P = 72/Q

When P = 8, the equation is 8 = 72/ Q. We solve by multiplying Q on both sides so

8Q = 72 and we can divide by 8 on both sides so Q = 9.