Variations table problems

Rules for calculating Variations In direct variation, = Constant In inverse variation, xy = constant Let us see some examples of how = constant in direct variation and xy = constant in inverse variation.

Direct variation Lets use x for bigger number and y for smaller number Look at the table given below: Weekly expenses x 2000 4000 6000 8000 No of people in the camp y 50 100 150 200 We see that x increases(↑ ), y also increases (↑ ). Next we shall find the ratio of ‘no of people in the camp’ to ‘weekly expenses’. =40 = constant = 40 = constant , Thus they are in direct variation Lets use x for bigger number and y for smaller number

Inverse variation Look at the table given below: Speed x 2 3 4 5 Time taken y 30 20 15 12 We see that speed x increases (↑ ), Time taken y decreases (↓). Next we shall find the product of Speed and Time taken. ‘Speed’ x ‘Time taken’ = xy = 2 x 30 = 3 x 20 = 4 x 15 = 5 x 12 = 60 = constant We see that , xy = 60 = constant, Thus they are in inverse variation

Example 1: If x varies directly as y, complete the given tables: 2 5 7 9 11 y 4 10 a 18 b Solution: Given: x varies directly as y ∴ In direct variation Lets find the constant and use it to find a and b and now lets find the unknown value a and b X 7 = ∴ a = 14 14 X 7 X 11 ∴ b = 22 = Ans: a = 14 , b = 22 X 11 22

Example 2: If x varies inversely as y, complete the given tables: 1 2 3 4 y 24 12 a b Solution: Given: x varies inversely as y ∴ In Inverse variation xy = constant Lets find the constant and use it to find a and b xy = 1 x 24 = 2 x 12 = 24 = constant Constant=24 and now, we try to find the unknown value a and b 3 x a = 24 3 x 8 = 24 ∴ a = 8 4 x b = 24 4 x 6 = 24 ∴ b = 6 Ans: a = 8 and b = 6

Try these If x varies directly as y, complete the given tables: X 9 18 21 b y 3 6 5 7 2. If x varies inversely as y, complete the given tables: X 1 2 3 4 6 Y 36 18 a 9 b