Question

If y varies directly with x, if x =9 when y = 18, how do you find x when y =24?

Answer 1

We can solve this using ration reasoning: `x_2/x_1=y_2/y_1`

Explanation:

If `x` varies directly with `y` (written `x prop y`), then doubling `y` means doubling `x`, so the rations of final values and initial values will be the same:

`x_2/x_1=y_2/y_1`

In this case,

`x_2/9=24/18`

`x_2=9*24/18 = 12`

Or, intuitively, if `x prop y` and `x = 9` when `y = 18`, we can conclude that

`x = 1/2y`

and `1/2` of 24 is 12.