Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 447

r=−− ±− −

= ±

()()()(,)

()

,

6209 6209 49738760

297

6209 38

2

5 551 681 15 038 880

194

6209 23 512 801

194

6209

,,− ,,= ± ,

= ±^44849

194

6209 4849

194

6209 4849

194

= +−,  = 75971 ,  7

The rate cannot be 7971 because the total round trip is only 8 hours

5 minutes. The professor’s average speed from Boston to New York is

57 mph. We want his time on the road from Boston to New York. His time

on the road from Boston to New York is^190190

57

(^313)
r
  =  hours or 3 hours = 
20 minutes.

Summary

In this chapter, we learned how to:

•   Solve number sense problems that involved products. We learned how to

solve number sense problems for which we are told either the sum/differ-

ence between two numbers or that they were consecutive and are then

told their product. We solve the product equation, which is reduced to

one variable with the information given in the problem. The product

equation is a quadratic equation.

•   Solve revenue problems. When given information about how a price

increase/decrease affects sales, we are asked what price will bring in some

desired revenue. We let x represent the number of increases/decreases in

the price, so the price and quantity sold can be represented by x. We then

use the model R = PQ, where P represents the price, and Q represents the

quantity. The revenue equation becomes a quadratic equation.

•   Solve work, distance, and geometry problems with quadratic equations. We

solved some problem types, such as work, distance, and geometry, in this

chapter using the same strategies that we learned in Chapter 8. The only

difference is that the models are quadratic equations.

•   Solve special distance problems. We used the Pythagorean theorem to solve

distance problems in which the bodies were moving on paths that form a

right angle. For stream problems, we used the following model.