Question

If y varies inversely as x and y = 5 when x = 10, how do you find y when x = 2?

Answer 1

`y=25`

Explanation:

`y=k/x` ;where `x` and `y` are variables and `k` is constant
or
`5=k/10`
or
`k=5(10)`
or
`k=50`
So Equation becomes `y=50/x`
When `x=2`
`y=50/2`
or
`y=25`

Answer 2

The equation is `y=50/x`

At `x=2;" "y=25`

Explanation:

There is a relationship between `y" and "x`

Mathematically this is written as `y color(white)(.)alpha color(white)(.) 1/x`

The `alpha` is stating that a relationship exists but as yet it is not totally defined

,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let `k` be the constants of variation

Write `y color(white)(.)alpha color(white)(.) 1/x` as: `" "y=kxx 1/x" " ->" " y=k/x`

You find the value `k` by substituting the values for the known condition `(x,y)->(10,5)`

Thus we have:

`y=kxx 1/x" " ->" "5=k/10`

Multiply both sides by 10

`10xx5=cancel(10)xxk/(cancel(10))`

`=>k=50`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So the equation is:

`y=50/x`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Thus at `x=2` we have:

`y=50/2=25`