Question

x varies inversely with y and x = 6 when y = 10.

What is the value of y when x = 8?

y=4/15

y=4.8

y=7.5 this is the correct answer but i don't understand why can someone please help me understand why

y=40/3

Answer 1

\(x\) varies inversely with \(y\) means that: \(\color{blue}{\displaystyle y=\frac{k}{x}}\)

Answer 2

You are given that when \(x=6\), then \(y=10\).
So, plug that in ...

Answer 3

Thank you so much this helps a lot!

Answer 4

\(\color{red}{\displaystyle x=6}\)
\(\color{green}{\displaystyle y=10}\)

\(\color{blue}{\displaystyle \color{green}{y}=\frac{k}{\color{red}{x}}\quad \Longrightarrow \quad \quad \color{green}{10}=\frac{k}{\color{red}{6}}}\)

Answer 5

You can solve for \(k\) (by multiplying times \(6\) on both sides).

Answer 6

\(\color{blue}{\displaystyle 10\color{red}{\times 6}=\frac{k}{6}\color{red}{\times 6}}\)

\(\color{blue}{\displaystyle 60=k}\)

Answer 7

So, we found the \(k\).

Answer 8

Therefore, you have the following inverse variation equation:

\(\color{blue}{\displaystyle y=\frac{60}{x}}\)

Answer 9

Now, (in the question) you are asked to find the value of \(y\), when \(x=8\).

To do this, plug in \(8\) instead of \(x\), and solve for \(y\).

Answer 10

thank you!

Answer 11

yw