If two variables x and y vary such that xy = constant(k). Then x and y are said to vary inversely or are in inverse variation.
If y varies inversely x, then directly as 1/x.
And x varies directly as 1/y.
Or, if x and y vary inversely, then x ¥ 1/y or y ¥
1/x.
Example:
x is varies inversely y and constant of variation is 1/2, find x when y = 5, find y when x = 1/4. Solution:
Since x is varies inversely y
We have x.y = k, given that k = 1/2.
\ xy = 1/2
If y = 5 Þ x.5 = 1/2 Þ x = 1/10.
If x = 1/4 Þ 1/4 . y = 1/2 Þ y 1/2 * 4 = 2
Example:
If 3 men can paint a house in 2 days, how long will it take 2 men to do the same job?. Solution:
This is an inverse relationship. The fewer men, the more days it will take to paint the house.
3:2 :: 2:x
or
3/2 = 2/x
Cross multiplying
3x = 4
x = 4/3 = 1 1/3 Answer: 1 1/3 days
Directions: Solve the following problems. Also write at least 10 examples of your own.