Question

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X varies jointly as w, y and z, if x = 18 when w = 2, y = 6 and z = 5 Find x when w = 5 y = 12 and z = 3.​

Answer 1

`\sf k = (3)/(10)`

`\sf x = 54` when
`\sf w = 5`,
`\sf y = 12`, and
`\sf z = 3`,

Explanation:

If
`\sf x` varies jointly as
`\sf w`,
`\sf y`, and
`\sf z`, the equation of variation is given by:

`\sf x = k \cdot w \cdot y \cdot z`

where
`\sf k` is the constant of variation.

To find the constant
`\sf k`, substitute the given values
`\sf x = 18`,
`\sf w = 2`,
`\sf y = 6`, and
`\sf z = 5` into the equation:

`\sf 18 = k \cdot 2 \cdot 6 \cdot 5`

`\sf 18 = 60 k`

`\sf k = (18)/(60)`

`\sf k = (3)/(10)`

Now that we have the constant of variation
`\sf k`, we can use it to find
`\sf x` when
`\sf w = 5`,
`\sf y = 12`, and
`\sf z = 3`:

`\sf x = (3)/(10) \cdot 5 \cdot 12 \cdot 3`

`\sf x = (3)/(10) \cdot 180`

`\sf x = 54`

Therefore, when
`\sf w = 5`,
`\sf y = 12`, and
`\sf z = 3`, the value of
`\sf x` is 54.