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
Let’s first understand direct variation
Direct variation occurs when two quantities change in the same manner
Video Examples: Joint Variation
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.
Direct variation between variables x and y can be expressed as:
y = kx, where ‘k’ is the constant of variation and k ? 0.
y = kxz represents joint variation. Here, y varies jointly as x and z.
More Examples on Joint Variation
y = 7xz, here y varies jointly as x and z
y = 7x2z3, here y varies jointly as x2 and z3
Area of a triangle = is an example of joint variation. Here the constant is ½. Area of a triangle varies jointly with base ‘b’ and height ‘h’
Area of a rectangle = l × w represents joint variation. Here the constant is 1. Area of a rectangle varies jointly with length ‘l’ and width ‘w’.
Solved Example on Joint Variation
Ques: 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.