Question

If x varies inversely with y and x = 8 when y = 10, find y when x = 6.

Answer 1

y=7.5?

Answer 2

y = k/x, where k is a constant

given y = 10 and x = 8. Use them to solve for k, then use the equation to solve for y when x = 6

Answer 3

Inverse variation of x and y implies \[y = \frac{k}{x}\] with \(k\) being the constant of variation. Plug in \(x=8, y=10\) and solve for \(k\). Use that value of \(k\) with \(x=6\) to find \(y\)

Answer 4

\[10=k/8 \]

Answer 5

Good, keep going...\(k=\)?

Answer 6

10*k=8?

Answer 7

\[10=\frac{k}{8}\]You want \(k\) all by itself, so multiply both sides by \(8\):
\[8*10 = \cancel{8}*\frac{k}{\cancel{8}}\]\[k=\]

Answer 8

80

Answer 9

Good, so the equation is \[y = \frac{80}{x}\]What does \(y=\) when \(x = 6\)?

Answer 10

13.3333?

Answer 11

So 40/3 is the answer

Answer 12

Thx @whpalmer4

Answer 13

Yes, it is, and for playing "solve that problem" today, we have a nice commemorative graph for your viewing pleasure!

Answer 14

lol