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

Answer:

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

Step-by-step 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

Answer 2

Answer:

The correct answer is B.

Step-by-step 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

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

$\implies 136=40k$

$\implies \frac{136}{40}=k$

$\implies \frac{17}{5}=k$.

The variation equation now becomes:

$y=\frac{17}{5}xz$

when x = 5 and z = 16, then

$y=\frac{17}{5}(5)(16)$

$y=17(16)$

$y=272$

The correct answer is B.