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I have a bag with blue marbles and yellow marbles in it. At the moment, the ratio of blue marbles to yellow marbles is 8:5. If I remove 12 blue marbles and add 21 yellow marbles, the ratio will be 1:3. How many blue marbles were in the bag before I removed some?

 Apr 16, 2018

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 #1
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B=Blue, Y=Yellow

B / Y =8/5,

[B -12] / [Y + 21] =1/3, solve for B, Y

B = 24    and     Y = 15 - What you originally started with.

 Apr 16, 2018
 #2
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B / Y  =  8/5   ⇒  B  = (8/5)Y

 

So

 

[ (8/5)Y - 12]  / [ Y + 21 ]  =  1/3      cross-multiply

 

(8/5)Y - 12  =  (1/3) [ Y + 21]

 

(8/5)Y - 12  = (1/3)Y + 7       

 

(8/5)Y - (1/3)Y  =  7 + 12

 

[24 - 5 ] Y / 15  =  19     ultiply both sides by  15

 

19Y  =  285       divide both sides by 19

 

Y  =  15 

 

B = (8/5)(15) =  24 

 

 

cool cool cool

 Apr 16, 2018

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