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

Answer:

Value of x = 400

Step-by-step 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;

$x = 2 \times (10)(20) = 2 \times 200$

Therefore, the value of x is, 400

Answer 2

Answer:

x = 400

Step-by-step 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 = $\frac{x}{yz}$ = $\frac{1200}{20(30)}$ = 2, thus

x = 2yz is the direct variation equation

when y = 10 and z = 20, then

x = 2 × 10 × 20 = 400