Question

X varíes directly with y and z. X =1200 when y =20 and z=30 find x when y=10 and z=20

Answer 1

x = 400

Explanation:

given that x varies directly with y and z the the equation relating them is

x = kyz ← k is the constant of variation

to find k use the given condition x = 1200 when y = 20 and z = 30

k =
`(x)/(yz)` =
`(1200)/(20(30))` = 2, thus

x = 2yz is the direct variation equation

when y = 10 and z = 20, then

x = 2 × 10 × 20 = 400

Answer 2

Value of x = 400

Explanation:

Joint variation states that describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them.

Given: x varies directly with y and z.

i.e
`x \propto y` and
`x \propto z`

then we have the joint variation as;

`x = k yz` ......[1] where k is the constant variation.

Substitute the value of x =1200 when y =20 and z = 30 to solve for k;

`1200 = k (20)(30)`

Simplify:

`1200 = 600k`

Divide both sides by 600 we get;

`k = 2`

Now, substitute k =2 , y =10 and z = 20 to find x;

Using [1] we have;

`x = 2 * (10)(20) = 2 * 200`

Therefore, the value of x is, 400