Examples for College Algebra and Geometry
These are examples to illustrate the Notes for College Algebra and Geometry prepared by M. Maheswaran, Department of Mathematics, University of Wisconsin - Marathon County.

CONTENTS

An Example of the Solution of an Applied ("Word") Problem

Problem 1:
Jack has a sum of $ 12,000. He invests part of it in an account A that pays a simple interest of 6% per year. He invests the remainder in an account B which pays a simple interest of 4% per year. At the end of one year he receives a total interest payment of $ 622. Write an equation to find the amounts invested in the two accounts. Then solve the equation to find the amounts.

Solution:
We shall use the stepwise procedure that we set out under applied problems in the Notes for College Algebra and Geometry.
Let x denote the dollar amount invested in account A. The basic equation for the quantities involved is:
amount of simple interest = principal sum * interest rate * number of years.
We shall set up a table to display the information we have. 

                      Account A    Account B
Principal sum $        x            12000 - x
Interest rate          0.06         0.04
Amount of interest $   0.06x        0.04 (12000-x)               

The last two add up to  622

Thus, our equation is    0.06x +  0.04 (12000-x) =  622.
That is,                     0.06x + 480 - 0.04x =  622.
We have                                    0.02x =  142.
Therefore                                      x =  7100.

Hence, the amount in account A is $ 7100  and the amount in account B is
$ (12000 - 7100), which is $ 4900.
CHECK:
Amount of interest on $ 7100 at 6% is $ 426 and the amount of interest on $ 4900 at 4% is $ 196. These add up to $ 622.

Go to Contents.
Go to Notes for College Algebra and Geometry.

Examples of the Solution of Absolute Value Inequalities

Problem 2:
Solve |3x+7| < 11.

Solution:
We can remove the absolute value sign and use the inequalities

                -11  <  3x+7  <  11.
These give 	-18  <  3x  <  4.
Thus,          	-6   <  x  <  4/3 .

The solution set is then   {x : -6 < x < 4/3}
Problem 3:
Solve |5x-12| > 8

Solution:
We remove the absolute value sign and rewrite as 

	       5x - 12  <  -8   OR	5x - 12  > 8 .
These give        5x  <  4	OR 	5x  >  20 .
Thus,	         x  <  4/5	OR	x  >  4 .

Hence, the solution set  is   {x :  x  <  4/5}  U  {x :  x  >  4} .

Go to Contents.
Go to Notes for College Algebra and Geometry.

An Example of the Solution of a Rational Inequality

ClickHERE for an example showing the application of the stepwise method described in the Notes.

Go to Contents.
Go to Notes for College Algebra and Geometry.

An Example of the Graph of a Rational Function

For an example of the graph of a rational function click HERE.

Go to Contents.
Go to Notes for College Algebra and Geometry.

Graphs of Conic Sections

The standard form of the equation, the graph and important features of each of the following conic sections are given in graphics format.

Go to Contents.
Go to Notes for College Algebra and Geometry.

(C) 1994
M. Maheswaran, University of Wisconsin Marathon County. last updated May 15, 1994