Question

Suppose `y` varies jointly as `x` and `z`. How do you find `y` when `x=6` and `z=8`, if `y=6` when `x` is 4 and `z` is 2?

Answer 1

`y = 36`

Explanation:

If `y` varies jointly as `x` and `z`, we can write this as

`y = kxz`

where `k` is the constant of proportionality (we'll be finding this)

In the situation, we're given that `y = 6` when `x = 4` and `z = 2`, so let's plug those in:

`6 = k(4)(2)`

`k = 3/4`

Now that we know the proportionality constant (which stays the same), we can use it in solving for `y` when `x` is `6` and `z = 8`:

`y = (3/4)(6)(8) = color(blue)(ulbar(|stackrel(" ")(" "36" ")|)`