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https://web2.0calc.com/questions/algebra_88471

 May 17, 2021
 #1
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Homer is giving some cookies to each of his three brothers. To the oldest, he gives half of the cookies and half a cookie. He then gives half of what is now left and half a cookie to his second brother. Finally, he gives half of what is now left and half a cookie to his second brother. At no time is a cookie broken or cut. How many cookies did Homer have to begin with? 

 

Let  the  total  number  of  cookies =  T

 

He  gives  the oldest  T/2  + 1/2

What  is  left  after  this  is  T  - (T/2  +  1/2)  =  (T/2) - 1/2

He  gives  the next brother  (1/2) ( T/2 -1 /2) + 1/2  =  T/4 + 1/4

What is left is  [  T/2  - 1/2 ] -  [ T/4  + 1/4 ]    = T/4 - (3/4)

He  gives  the last  brother  (1/2)  [ T/4  - (3/4)]  + 1/2   =  T/8 + 1/8

 

Now  the  sum of what  he gives  to each  brother  must  be  the  total number  of cookies

 

So....we  have  this  equation

 

T/2 + 1/2    +   T/4  + 1/4   +  T/8 +  1/8    =  T       simplify

 

(7/8) T  +  (7/8)   = T

 

(7/8)  =  T(1 - 7/8)

 

7/8  =  T/8

 

7  =  T     = the  number  he statred with

 

Proof

He  gives the oldest  (1/2) 7  + 1/2 =   4

3 are left

 

He  gives  the  next     (1/2) 3  + 1/2   =  2

1 is left

 

He  gives  the last  brother  (1/2) 1  + 1/2  =  1

 

 

cool cool cool

 May 17, 2021

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