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Kamal and Jason had 128 marbles altogether. Kamal gave away three times as many marbles as Jason. The marbles Jason had left was 4 fewer than the marbles he gave away. Jason had three times as many marbles left as Kamal. How many marbles did Jason have at first?

 May 6, 2021
 #1
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Let  the  number of  marbles  that Kamal  had  in the  beginning=  K

Then  Jason had (128 - K)

 

Let the  number  of  marbles  that  Jason gave away =  G

Then the  number of marbles  that Kamal  gave away =  3G

And  the number that  Kamal had left = K  - 3G

 

And  we  know that, from Jason's point of view

 

What  he started with - what  he gave away =  what he had left

 

(128 - K)  -  G   = G - 4  simplify

 

(128 - K)   =  2G - 4

 

128  + 4  -  2G   = K   

 

132  -  2G     =    K       (1)

 

And  from  Kamal's   point of  view  we have  that

3 times  what  he  had left = what Jason had left

 

3(K - 3G)  =  G -  4       (2)

 

Sub  (1)  into (2)

 

3  (  132 - 2G - 3G)  =  G - 4

 

396 - 15G  = G  -  4

 

400  =  16G

 

G = 400/16  =   25

 

What Jason started with   =  2G  - 4   =  2*25 - 4   =  46

 

 

cool cool cool

 May 6, 2021

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