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PSME 95 - Final Project

 Yu-Jeng (Dennis) PanRaeda Ashar 

!o" to sol#e $or % and & in a s&ste' o$t"o euations $or a "ord ro*le'

(MA+! ,./,,)

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0atch 1ideo on Sol#ing S&ste's *& Su*stitution - Math !elhtt2//"""3&outu*e3co'/"atch4#67""u5"jcaA

http://www.youtube.com/watch?v=KNwwu5wjcaAhttp://www.youtube.com/watch?v=KNwwu5wjcaA

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Sol#e the "ord ro*le' $or ho'e"or

Suppose a wealthy American CEO of a financial company earns $1million from his paycheck each year. His annual net income equals to$1million minus the annual expense. From his past experiences he!elie"es that his annual expense equals to #% of his annual netincome plus $1&&&& annual fees on insurance.

 

 As the CEO's accountant !ase( on the a!o"e information you must(etermine the CEO's annual net income an( annual expense.

 

But many tutees are afraid of word problems. Some have trouble

reading text in the word problem, and some simply have word

problem anxieties and refuse to even looking at it.

 

0ord Pro*le'

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8reas 0ord Pro*le' into S'all Parts

To help tutees to understand what the word problem wants the tutees to do,

the tutor can break the word problem into small part. For this example wordproblem, the tutor can break it into 4 parts

!"# $ %&' earns (" million ) year.

!*# +is annual net income (" million minus the annual expense.

!-# +is annual expense */ of his annual net income plus ("0000.

!4# Find %&'1s annual net income and annual expense.

 

2ive tutees *0 seconds to read these 4 parts. $fter they are done, the tutorshould ask tutees to answer a series of 3uestions to solve the world problemstep by step very suitable for tutees who are se3uential learners.

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Ste ne

3) 0hat are the , #aria*les "e need to sol#e in the "ord ro*le'4 

,3) Su*stitute the #aria*les in ter's o$ : and Y

;3) +he "ord ro*le' is *asicall& a s&ste' o$ t"o euations3Please set u the s&ste' o$ t"o euations3

 

First #aria*le is s annual net inco'e3?

Another #aria*le is s annual e%ense3?

 Y =E>s annual net inco'e

: =E>s annual e%ense

 Y ...... @ :

: .3,5Y ....

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Ste +"o

B3) 0e $irst sol#e $or Y3 8ut !o"4

53) Cet us use Alge*ra to sol#e $or Y

 

3) Y is =E>s annual net inco'e3 So =E>s annual net inco'e is2

+o sol#e $or Y lug : .3,5Y .... into the : #aria*le

in Y ...... @ :3 And got2

 Y ...... @ .3,5Y @ ....

 Y ...... @ .3,5Y @ ....

 Y 99.... @ .3,5Y

3,5Y 99....

 Y 99.... / 3,5 Y 9,...

 

+he =E>s annual net inco'e is Y G9,...

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Ste +hree

3) A$ter no"ing Y 9,... sol#e $or :3 8ut !o"4

H3) : is =E>s annual e%ense3 So =E>s annual e%ense is2

A$ter getting Y 9,... lug Y 9,... into

: .3,5Y .... to sol#e $or :2

: .3,5Y ....

: .3,5 (9,...) ....

: 9H... ....: ,.H...

+he =E>s annual e%ense is : G,.H...

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Don>t Forget to =hec 0orI

A$ter $inding out that Y G9,... and : G,.H... lug : and Y intothe original s&ste' o$ t"o euations to chec "or2

And it "ors and so Y G9,... and : G,.H... is the solution to the

s&ste' o$ t"o euations "e need sol#e3

  Y ...... @ : Y ...... @ ,.H... Y 9,...

: .3,5Y .... : .3,5(9,...) .... : ,.H...

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=onclusion

0e are sure that the ans"er $or the "ord ro*le' is that $or the=E the annual net inco'e is Y G9,... and the annual e%enseis : G,.H...3