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
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
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