Variation and Proportion Indirect Proportion The formula for

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: Ø 1. 2. 3. 4. Write the equation: y = k/x Substitute for x and y Solve for k 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. 2. 3. 4. Write the equation: y = k/x Substitute for x and y Solve for k Rewrite the equation with k as the constant y = k/x 145 = k/. 8 145(. 8) = k, or k =116 y = 116/x

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. Ø y = time; x = number of people 1. 2. 3. y = k/x 4 = k/20 4 • 20 = k, or k = 80 Ø Equation: l y = 80/x

Practice Problems: Answers 1. y = 25 when x = 3 Ø 2. y = 45 when x = 2 Ø 3. Equation: y = 90/x y = 80 when x =. 7 Ø 4. Equation: y = 75/x Equation: y = 56/x y =. 8 when x = 4 Ø 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? 1. Write the equation: y = k/x Substitute for x and y Solve for k Rewrite the equation with k as the constant 2. 3. 4. y = k/x 16 = k/2 16(2) = k, or k =32 y = 32/x