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There were some green and red apples in a box. Ted took up 2/11 of the green apples from the box. He replaced each of these green apples taken out with red apples. After that, he took out 2/5 of the green apples and 1/3 of the red apples. There were 108 green apples and 228 red apples left in the box in the end. What was the total number of green and red apples in the box at first?

 May 17, 2021
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Let  the  original  number  of  red apples  =  R    and  the original  number  of green apples =  G

 

We  have  that

 

R   +  (2/11)  G   -  (1/3)[ R + (2/11)G ]  =  228

G  - (2/11)G -  (2/5)  [ G -(2/11)G ]     =108

 

Looking  at  the  second  equation and  simplifying  we  have

 

(9/11)G  - ( 2/5)G  +  (4/55) G =   108

( 45/55)G  - (22/55)G  + ( 4/55)G    =108

(27/55) G  =108

G =  108  / 27  *  55   =  220  =  original number  of green apples

 

And  simplifying the  first  equation we  have

 

R  + (2/11)(220)  -  ( 1/3)  [ R  + (2/11)(220)]  =  228

 

R  +  40   -  (1/3)R  - (1/3) (40)  = 228

 

(2/3)R  +  40  - 40/3  =  228

 

2R  + 120  - 40  =   684

 

2R  +  80   =  684

 

2R  =  604

 

R  =  604  / 2    =  302   =  original number of  red apples

 

R + G =      302   +  228    =    530

 

 

cool cool cool

 May 17, 2021

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