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In a bag with $20$ marbles, five of them are blue. How many blue marbles must be added to the bag so that the probability of selecting a blue marble at random is $\frac{5}{8}$?

 Aug 5, 2023

Best Answer 

 #2
avatar+129316 
+1

Let   B  be the number of blue matbles that we need to  add

 

So

 

Total Blue  / Total Number of marbles =   5/8

 

[5 + B ] / [ 20 + B ]   = 5/8     

 

5 + B =  (5/8) ( 20 + B]    nultiply both sides by 8/5

 

8 + (8/5) B  = 20 + B

 

(8/5)B - B = 20 - 8

 

(3/5)B = 12

 

B = 12 * (5/3)  =  60 / 3 =  20

 

We need to add 20 blue marbles

 

Proof

 

[5 + 20 ] / [ 20 + 20]  =  25 / 40  =  5 / 8

 

cool cool cool

 Aug 5, 2023
 #2
avatar+129316 
+1
Best Answer

Let   B  be the number of blue matbles that we need to  add

 

So

 

Total Blue  / Total Number of marbles =   5/8

 

[5 + B ] / [ 20 + B ]   = 5/8     

 

5 + B =  (5/8) ( 20 + B]    nultiply both sides by 8/5

 

8 + (8/5) B  = 20 + B

 

(8/5)B - B = 20 - 8

 

(3/5)B = 12

 

B = 12 * (5/3)  =  60 / 3 =  20

 

We need to add 20 blue marbles

 

Proof

 

[5 + 20 ] / [ 20 + 20]  =  25 / 40  =  5 / 8

 

cool cool cool

CPhill Aug 5, 2023

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