Joint Variation

Definition of Joint Variation

  • Joint variation is a variation in which y varies jointly as x or powers of x () and y or powers of z ( ), if there is some nonzero constant k such that , where x ≠ 0, z ≠ 0, and n > 0.

Examples of Joint Variation

  • y = 7xz, here y varies jointly as x and z.
  • , here y varies jointly as and .

Solved Example on Joint Variation

Assume a varies jointly with b and c. If b = 2 and c = 3, find the value of a. Given that a = 12 when b = 1 and

c = 6.

Choices:

A. 2

B. 3

C. 12

D. 24

Correct Answer: C

Solution:

Step 1: Given that a = 12 when b = 1 and c = 6.

Step 2: As a = kbc, .

Step 3:  For b = 2 and c = 3, a = k × 2 × 3 = 2 × 2 × 3 = 12.

Related Terms for Joint Variation

  • Variable
  • Constant
  • Power

Real-world Connections for Joint Variation

  • Force = mass × acceleration. The force exerted on an object varies jointly as the mass of the object and the acceleration produced.

Additional Links for Joint Variation