Question

If x varies inversely as y and directly as t, and x =12 when t =10 and y =25, how do you find y when x is 6 and t= 3?

Answer 1

This is the only way I could think of that made the question work.
Someone else may differ on this.

`y=15`

Explanation:

`x` varies inversely as `ycolor(white)("d") ->color(white)("dd") x=k/y" "..Eqn(1)`

and directly as t `color(white)("ddddd")->color(white)("dd")x=ct" "..Eqn(2)`

Given that `x=12` when `t=10 and y=25`

Lets try combining these.

Consider `x=k/y`

Could the question be stating that the `k` represents the 'varies directly part in which case we would have:

`x=(ct)/y larr" which combines "Eqn(1) and Eqn(2)`

Thus for initial condition we have: `c=(xy)/t = (12xx25)/10 = 30`

Consequently we have:

`x=(30t)/y color(white)("dddd")=>color(white)("dddd")y=(30t)/x`

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Find `y` when `x=6 and t=3`

`=>y=(30xx3)/6=15`