p p varies inversely as q q , and p = 18 p=18 when q = 9 q=9 . If q = 12 q=12 , what is the value of p p ?

this problem, we are told that p varies inversely as q. We're told p equals 18 when q equals nine, and we're told if q is equal to 12, what is the value of p? So there's a lot of words that we got there, but basically, let's start with what we know. We have that p varies inversely as q. We should know that this means we are dealing with an inverse variation problem. So we have p is going to be related to q, And then what we'll have on top here is this constant of variation k. Now we are told that p is equal to 18, and at that same moment, q is equal to nine. So take this p and replace it with 18, and then I'll take this q and replace it with nine. Now what I need to do from here is solve for k. Well-to-do that I'm gonna multiply nine on both sides of the equal sign. That'll get the nines to cancel on the left side, leaving me with just k. And we have k is equal to nine times 18, which you can check that on a calculator if you want to, that comes up to 162. So we now have our value of k. So now that we have k, from here we are asked if q is equal to 12, what is the value of p? So what that means is going back to my equation, we have that p is equal to k over q, which is the same thing as 162 over q, because we just found this k value. So this is the relationship that relates p and q, and if I want to solve this part of the problem which asks for a q value of 12, well that just means I need to take that q and replace it with 12. So we get that p is equal to 162 over 12, which if you type that into a calculator it comes up to 13.5. So 13 and a half which is the same thing as 27 over two as a reduced fraction. So either one of these would be the solution to this problem.

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Multiple Choice

$p$ varies inversely as $q$ , and $p equals 18$ when $q equals 9$ . If $q equals 12$ , what is the value of $p$ ?

13.5

162

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pp varies inversely as qq, and p=18p=18 when q=9q=9. If q=12q=12, what is the value of pp?

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$p$ varies inversely as $q$ , and $p equals 18$ when $q equals 9$ . If $q equals 12$ , what is the value of $p$ ?