Question

If 4/3 X-2/3Y=2, what is the value of 16X/4Y?

Answer 1

If I am reading the equation correctly (see below) it can be simplified to `6/Y+2` but not evaluated.

Explanation:

I hope the equation reads `(4X)/3 - (2Y)/3 = 2` (the second term is not clear). If so, we can multiply each term by 3, to get

`4X-2Y=6` and the denominators are removed.

Now, solve for X (or rather, 16X):

`4X=6+2Y`

Multiply through by 4:

`16X = 24+8Y`

Now, the numerator in the second expression can be replaced:

`(24+8Y)/(4Y)=(6+2Y)/Y`

or, `6/Y+2`

Answer 2

It is an infinite range of values because the original expression is a line. In terms of the Y term, it is:
`2Y + 6/Y`
In terms of X it is:
`(16X)/(8X - 12)`
The line is `Y = 2X - 3`
It may also be simplified as an expression to `(4X)/Y`

Explanation:

First, rearrange the given equation to give you the ratio of `X/Y`, then apply the desired multiplier.
`4/3X - 2/3Y = 2` Multiply by 3:

`4X - 2Y = 6` ; `4X = 2Y + 6` Divide by 2:

`2X = Y + 3` and/or `Y = 2X - 3` or `X = Y/2 + 3/2` Substitute into the desired ratio.

`(16X)/(4Y)` `(16X)/(4(2X - 3)) = (16X)/(8X - 12)`

`(16X)/(4Y)` `(16(Y/2 + 3/2))/(4Y) = (8Y + 24)/(4Y)`

`2Y + 6/Y`