# FIND CONSTANT OF VARIATION

The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another.

If x varies directly to y, then y = kx.

Constant of variation k = y/x

If x varies inversely to y, then y = k/x.

Constant of variation k = yx

In each case one value is given for each of two variables that vary directly. Find the constant of variation.

Problem 1 :

x = 12, y = 3

Solution :

x = 12, y = 3

y = kx

k = y/x

k = 3/12

k = 1/4

Problem 2 :

d = 120, t = 3

Solution :

d = 120, t = 3

t = kd

k = t/d

k = 3/120

k = 1/40

Problem 3 :

y = 2, z = 18

Solution :

y = 2, z = 18

z = ky

k = z/y

k = 18/2

k = 9

Problem 4 :

p = 12.8, s = 3.2

Solution :

p = 12.8, s = 3.2

s = kp

k = s/p

k = 3.2/12.8

k = 0.1/0.4

k = 0.25

Problem 5 :

t = 12, n = 8

Solution :

t = 12, n = 8

n = kt

k = n/t

k = 8/12

k = 2/3

Problem 6 :

I = 51, t = 6

Solution :

I = 51, t = 6

t = kl

k = t/I

k = 6/51

Problem 7 :

s = 88, t = 110

Solution :

s = 88, t = 110

t = ks

k = t/s

k = 110/88

k = 5/4

Problem 8 :

A = 212, P = 200

Solution :

A = 212, P = 200

P = kA

k = P/A

k = 200/212

k = 50/53

Problem 9 :

r = 87, s = 58

Solution :

r = 87, s = 58

s = kr

k = s/r

k = 58/87

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