Question

y varies inversely as three times x. When x = 6, y = 2. Find x when y = 12.

A. x = 1
B. x = 3
C. x = 6
D. x = 9

Answer 1

Varying inversely means it looks like

\[\large y = \frac{k}{x}\]

Answer 2

So if it varies 3 times x we have

\[\large y = \frac{k}{3x}\]

Answer 3

If we plug x = 6 into their equation we get this:

y = 36x
y = 36(6)
y = 216.

Certainly, using their equation, y does not equal 2 when x = 6.

y = k [1/(3x)]
y = k/(3x).

The last equation above expresses y in terms of x, but it doesn't tell us exactly how they relate. For any variation problem, there is a constant of variation, k, which relates how the quantities vary with each other as they change. Before we can solve the problem, we first have to find k. We can do that by plugging in y = 2, and x = 6, and solving for k's value:

2 = k/(3∙6)
2 = k/18
2(18) = k
36 = k.

The equation of variation then is this:

y = 36/3x
y = 12/x
Above we canceled a factor of 3 in the numerator and denominator.

Now we can find x when y = 12:

y = 12/x
x = 12/y
x = 12/12
x = 1.

So when y = 12, x = 1.

Hope this helps !!- Bree :) (from yahoo.com)

Answer 4

Now we know that x = 6 when y = 2...so plug those in and solve for 'k'

\[\large 2 = \frac{k}{3(6)}\]
\[\large 2 \times 18 = k\]
\[\large k = 36\]

Answer 5

Oh...nvm lol

Nice work @Bookworm14 :)

Answer 6

thank you, I knew some of it but I had to look up the rest lol