Variation and Proportion

Indirect Proportion

The formula for indirect variation can be written as y=k/x where k is called the

constant of variation.

***We can follow the same steps from direct variation!!

The steps to follow to solve a problem with indirect variation:

1. Write the equation: y = k/x2. Substitute for x and y3. Solve for k4. Rewrite the equation with k as the constant

Problem:Find an equation of indirect variation where

y varies indirectly as x. One pair of values is y = 145 when x = .8.

1. Write the equation: y = k/x y = k/x2. Substitute for x and y 145 = k/.83. Solve for k 145(.8) = k, or k =1164. Rewrite the equation with k y = 116/x as the constant

Problem:The time (t) required to do a certain job varies inversely as the number (n) of people working (assuming all work at the same rate). It takes 4

hours for 20 people to wash and wax the floors in a building. Find the equation of variation.

y = time; x = number of people

1. y = k/x2. 4 = k/203. 4•20 = k, or k = 80

Equation: y = 80/x

Practice Problems: Answers

1. y = 25 when x = 3 Equation: y = 75/x

2. y = 45 when x = 2 Equation: y = 90/x

3. y = 80 when x = .7 Equation: y = 56/x

4. y = .8 when x = 4 Equation: y = 3.2/x

Practice Problems: Answers (Continued)

5. It takes 16 hours for 2 people to resurface a gym floor. How long would it take 6 people to do the job?

6. Write the equation: y = k/x y = k/x7. Substitute for x and y 16 = k/28. Solve for k 16(2) = k, or k

=329. Rewrite the equation with k y = 32/x as the constant