Question

the quantity y varies directly as x and inversely as z. when x is 10 and z is 4, y is 15. what is y when x is 20 and z is 6? 1) 6 2) 20 3) 27 4) 30

Answer 1

Answer:

Option 2nd is correct

y = 20

Step-by-step explanation:

Joint variation says that:

if $y \propto x$ and $y \propto \frac{1}{z}$

⇒$y \propto\frac{x}{z}$

then;

equation is in the form of :

$y = k \cdot \frac{x}{z}$ where, k is the constant of variation.

As per the statement:

the quantity y varies directly as x and inversely as z.

then by definition we have;

$y = k \cdot \frac{x}{z}$         .....[1]

When x = 10, z = 4 and y = 15

Substitute these in [1] we have;

$15 = k \cdot \frac{10}{4}$

⇒$15 = 2.5k$

Divide both sides by 2.5 we have;

6 = k

or

k = 6

then;

$y = 6 \cdot \frac{x}{z}$    

we have to find y, when x = 20 and z = 6

Substitute these we have;

$y = 6 \cdot \frac{20}{6}= 20$

⇒y = 20

Therefore, the value of y = 20