JOINT VARIATION

Definition of Joint Variation

Joint variation is the same as direct variation with two or more quantities.

    That is:
    Joint variation is a variation where a quantity varies directly as the product of two or more other quantities
    Lets first understand direct variation
    Direct variation occurs when two quantities change in the same manner

Video Examples: Joint Variation


    That is:
    Increase in one quantity causes an increase in the other quantity
    Decrease in one quantity causes a decrease in the other quantity
    For Example:
    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 . 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.

Solution:

    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
    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
    Step 5: So, when a varies jointly with b and c and If b = 2 and c = 3, then the value of a is 12.