Example of joint variation in algebra, showing how y varies jointly with x and z.

You're given a joint variation problem, where:

> y varies jointly as x and z, which means:
> y = k·x·z
> for some nonzero constant k.

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Step 1: Use the given values to find k

We’re told that when x = 4 and z = 3, then y = 20.

Plug these into the equation:

> 20 = k · (4) · (3)
> → 20 = 12k

Now solve for k:

> k = 20 / 12 = 5/3

✔ So the constant of variation is k = 5/3

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Step 2: Use k to find y when x = 2 and z = 3

Now plug into the formula:

> y = k·x·z = (5/3) · (2) · (3)

Simplify:

> First, multiply 2 and 3: → (5/3) · 6
> Then: (5 × 6) / 3 = 30 / 3 = 10

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✔ Final Answer: y = 10

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💡 Explanation Summary:

- Joint variation means y is proportional to the product of x and z.
- We first used the known values to find the constant k.
- Then we used k with the new values of x and z to compute the new y.
- The key idea: k stays the same — it’s the “constant of proportionality”.

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✔ So, when x = 2 and z = 3, y = 10.