Definition of Joint Variation
Joint variation is the same as direct variation with two or more quantities.
Joint variation is a variation where a quantity varies directly as the product of two or more other quantities.
Direct variation occurs when two quantities change in the same manner.
Increase in one quantity causes an increase in the other quantity.
Decrease in one quantity causes a decrease in the other quantity.
The cost of a pencil and the number of pencils you buy.
Buy more pay more….Buy less pay less.
y = kx, where ‘k’ is the constant of variation and k ≠ 0.
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.
Step 1: First set up the equation. a varies jointly with b and c
a = kbc
Step 2: Find the value of the constant, k.
Given that a = 12 when b = 1 and c = 6
a = kbc
12 = k × 1 × 6
Þ k = 2
Step 3: Rewrite the equation using the value of the constant ‘k’.
a = 2bc
Step 4: Using the new equation, find the missing value.
If b = 2 and c = 3, then a = 2 × 2 × 3 = 12.
So, when a varies jointly with b and c and If b = 2 and c = 3, then the value of a is 12.
Force = mass × acceleration. The force exerted on an object varies jointly as the mass of the object and the acceleration produced.