Z varies inversely with x and directly with y. If x = 4, y = 48 and 2 = -2, find x when z = 8 and y = 96.

Value of x = 5 .

Step-by-step explanation:

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

Given: x varies directly with y and inversely with z.

i.e x \propto yx∝y and x \propto \frac{1}{z}x∝

z

1

then we have the combined variation as;

x = k\frac{y}{z}x=k

z

y

[1] where k is the constant variation.

Substitute the value of x =20 when y =8 and z = 4 to solve for k;

20 = k\frac{8}{4}20=k

4

8

Simplify:

20 = 2k20=2k

Divide both sides by 2 we get;

k = 10k=10

Now, substitute k =10 , y =4 and z = 8 to find x;

Using [1] we have;

x = 10 \times \frac{4}{8} = 10 \times \frac{1}{2} = 5x=10×

8

4

=10×

2

1

=5

Therefore, the value of x is, 5

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