Inverse Variation
As the price of an item increases, its sales decrease. This is an example of inverse variation. An inverse variation problem has one constant of variation, but is divided instead of multiplied.
Practical Problem: Threshold Weight
Direct variation is used in a practical problem to find the threshold weight for men of different heights.
Practical Problem: The Amount of Weight a Shelf Can Hold
The amount of weight a shelf can hold varies with the length, width, and thickness of the board. Finding how much weight a specific board can hold combines direct, joint, and inverse variation and is illustrated here.
Practical Problem: The Speed of Two Pulleys
A practical problem involving the speeds of two pulleys of different diameters is solved using inverse variation.
Practical Problem: How Much Weight Can One Beam Hold?
The amount of weight a beam can hold varies with its length, width, and thickness. The load capacity for a beam that is laying flat is compared with the load capacity for the same beam when it is placed on edge.
Combining Direct, Joint, and Inverse Variation in a Problem
A problem combining direct, joint, and inverse variation is demonstrated and solved.
Variation Problems
A variation problem always involves two sets of information and two formulas. To solve a variation problem, a general formula is written from the variation statement. A specific formula can then be written with the constant of variation.
Using Proportion to Find Real Lengths from Scale Lengths
A specific formula is developed to solve a practical problem of converting scale length to real length in a scale drawing.