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I have a bag with yellow and blue marbles in it. At the moment, the ratio of blue marbles to yellow marbles is 4:3. If I add 5 blue marbles and remove 3 yellow marbles, the ratio will be 13:3. How many blue marbles were in the bag before I added more?

 Jul 7, 2022
 #1
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Call the total number of  marbles in the  bag before we added any  N

The blue  ones=  (4/7)N

The yellow =  (3/7)N

 

So

 

[ (4/7)N + 5 ]          13

__________  =   ____    cros-multiply

[ (3/7)N - 3 ]            3

 

 

3 [ (4/7)N + 5 ]  =  13 [ (3/7)N - 3 ]    

 

(12/7)N + 15  =  (39/7)N - 39

 

(39/7)N - (12/7)N  = 15 + 39

 

( 27/7)N =  54

 

N =  54 ( 7/27)  =  14

 

The number of blue originally =  (4/7)(14)  =   8

 

 

cool cool cool

 Jul 7, 2022

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