Inverse proportion - Word Problem

Question

Question: given that $B^2$ is inversely proportional to $A+3$ and $B$ is always positive, find the value of $B$ when $A=17$ if $B=5$ when $A=2$.

I am so confused on how to work out this question. I know this is a pretty easy question to all of you. But I find this very confusing. Can someone explain to me what I need to do and how I do it ?

Sorry for the nooby question.

Answer 1

Inverse proportion means that $B^2 * (A + 3) = k$.

When dealing with these kinds of questions, you are basically doing the following:

Substitute $k$ with the same inverse proportion but different values.

So, $B_1^2 * (A_1 + 3) = B_2^2 * (A_2 + 3)$. We'll plug in for $B_2, A_2, A_1$ and solve for $B_1$.

$B_1^2 * (17 + 3) = 5^2 * (2 + 3)$

So, we get $B_1^2 * 20 = 125 \to B_1^2 = \frac{125}{20} \to B_1 = \sqrt{\frac{125}{20}}$, and then you just take the positive of that square root (it'll give you positive anyways, so you're set.)

Answer 2

Saying $B^2$ is inversely proportional to $A+3$ means $B^2=\frac k{A+3}$ or $B^2(A+3)=k$. You are give a data point, $A=2,B=5$, which lets you evaluate $k$. Then plug in $A=17$ and evaluate $B$.