Algebra and Trigonometry, 5th Edition

2.6 Variation and Applications

• Find equations of direct variation, inverse variation, and combined variation given values of the variables.

• Solve applied problems involving variation.

We now consider applications involving variation.

Direct Variation

The median hourly wage for an elevator and escalator installer/repairer is $35 per hour (Source: U.S. Bureau of Labor Statistics). In 1 hr, $35 is earned; in 2 hr, $70 is earned; in 3 hr, $105 is earned; and so on. This gives rise to a set of ordered pairs:

$$(1,35),(2,70),(3,105),(4,140),\text{and so on}.$$

Note that the ratio of the second coordinate to the first coordinate is the same number for each pair:

$$\frac{35}{1}=35,\frac{70}{2}=35,\frac{105}{3}=35,\frac{140}{4}=35,\text{and so on}.$$

Whenever a situation produces pairs ...