Question

Suppose Z Varies directly with x and inversely with y, where x = 16, y = 4, when z = 32...............

a.) Write an equation for this variation.
b.) Find Z When x = 21 and y = 6
c.) Find X when y = 48 and z = 4

Answer 1

a.)
Z = kx/y where k is a constant.
32 = 16k/4
k = 128/16
k = 8

z = 8x/y

b.)
Z = 8(21)/6
Z = 28

c.)
4 = 8x/48
x = 192/8
x = 24

Answer 2

Let ¢ be our symbol of variation.
So Z ¢ X/Y
Hence Z = KX/Y Where K is our constant of proportionality.
So Z = 32 and X = 16 and Y = 4
32 = K * 16/ 4
K = 32 * 4/ 16 = 8

So Z = 8 * 21/6 = 28
On the other hand 4 = 8 * X/48
So X = 48 * 4/8 = 24