Substitution and Elimination

WebPages

by Giovanna Rigo

and

Lindsay Johanson

 

       We chose to do substitution and elimination for this web page assignment because we felt that everyone should know and understand how to solve equations using these two processes.  Also, we think that it’s an interesting method of algebra II.  Hopefully you will enjoy this great learning experience in the same way we did.

 

!Substitution:                

                                   

Example 1 (for substitution)

          A footwear company is preparing to market a new kind of sports shoe.  The company plans to spend $28 million on advertising.  Past experience shows that the amount spend on television advertising should be 3.5 times as much as the amount spent on magazine advertising.  Determine how much money should be spent on each type of advertising.

                                                                   

Solution:                                                    

28 million

3.5 * magazine = tv

 

Step one -                             Step two using substitution –

t+m=28                                   substitute 3.5m for t

t=3.5m                                    (3.5m)+m=28

                                        4.5m=28

                                        m is about 6.22

Step three –

t=3.5m

t=3.5(6.22)   substitute 6.22 for m to find out t.

t is about 21.78

 

Answer: company should spend about $21.78 million on television advertising and about $6.22 million on magazine advertising.

 

***This problem applies to day-to-day life and shows how someone could use substitution in other places and circumstances outside of the Algebra II class.

 

!Elimination:

 Example 1 (for elimination)

          Jared’s boat doesn’t have a speedometer, so he timed how long it took to travel one nautical mile (nm) with as river’s current. (Downstream) And 1mn against it (upstream).  While keeping his boats engine running at a constant 3000 rev per minute.  (As measured on the boat’s tachometer). 

          Use Jared log to determine the speed of his boat in still water when the engine runs at 3,000 rev per minute and find the speed of the current.

	Downstream	Upstream
Time (min/sec)	3:12	3:22
Speed (knots)	18.8	17.8

 

 

Step one : write two equations

S + W=18.8  ----> combined downstream speed

S - W=17.8  -----> combined upstream speed

 

Step Two: solve by using addition and add corresponding sides of each equation to eliminate the variable W

S + W = 18.8

S – W =17.8

-----------------

2s       = 36.6                 s = 18.3

 

After this step use substitution and substitute 18.3 for S

 

18.3 + W = 18.8           w = 0.5

 

The answer is s = 18.3 and w = 0.5.

 

*** This problem, along with the one for substitution, can also be applied to day-to-day life for people who really do care about what the speed is and don’t have a speedometer.

 

Seven Links Related to Substitution & Elimination

 

1.     http://mathforum.org/library/drmath/view/57307.html

 

2.   http://em-ntserver.unl.edu/Math/mathweb/algebra/algesb97.html#Systems

 

3.   http://bus.colorado.edu/mba/admissions/mathreq/systems.cfm

 

4.  http://www.sci.wsu.edu/~kentler/Fall97_101/nojs/Chapter4/section1.html

 

5.   http://www.glencoe.com/sec/math/algebra/algebra1/algebra1_01/pdf/0802.pdf

 

6.  http://mcraefamily.com/MathHelp/BasicWordProblemsSubstitution.htm

 

7. http://www.sosmath.com/soe/SE2001/SE2001.html