Question

Suppose y varies jointly as x and z. Find y when x = 5 and z = 16, if y = 136 when x = 5 and z = 8. Round your answer to the nearest hundredth, if necessary.

Answer 1

The correct answer is B.

Explanation:

If y varies jointly as x and z, then we can write the join variation equation.

`y=kxz`, where 'k' is the constant of proportionality.

If y = 136 when x = 5 and z = 8,then

`136=k(5)(8)`,

`\implies 136=40k`

`\implies (136)/(40)=k`

`\implies (17)/(5)=k`.

The variation equation now becomes:

`y=(17)/(5)xz`

when x = 5 and z = 16, then

`y=(17)/(5)(5)(16)`

`y=17(16)`

`y=272`

The correct answer is B.

Answer 2

The value of y when x = 5 and z = 16 is 272

Explanation:

* Lets Talk about the direct variation

- y is varies jointly (directly) as x and z, that means there are direct

relation between y , x and z

- y increases if x increases or z increases

∴ y ∝ x × z

- To change this relation to equation we use a constant k

∴ y = k (x) (z), where k is the constant of variation

- To find the value of k we substitute the values of x , y and z in

the equation above

∵ y = 136 when x = 5 and z = 8

∴ 136 = k × 5 × 8

∴ 136 = 40 k ⇒ divide both sides by 40

∴ k = 3.4

- Substitute this value in the equation

∴ y = 3.4 (x) (z)

∵ x = 5 , z = 16

∴ y = 3.4 (5) (16) = 272

∴ The value of y when x = 5 and z = 16 is 272