+0  
 
+1
32
1
avatar

A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag?

 Jan 8, 2020
 #1
avatar+106519 
+1

Let  the original   number of red marbles  =  R  and the number of  original number of  blue marbles = B

 

And   we know that

 

  R               1

_____  =    ___        cross-multiply   and we have that

R + B           5

 

5R  = R + B          subtract  R from both sides

 

4R  = B            (1)

 

And after 5 red marbles are added to the bag we have that

 

R +  5                    1

_________  =      _____      cross-multiply

R + B + 5                3

 

3(R +5)  =  R + B + 5

 

3R + 15  =  R + B + 5        subtract  R  from both sides

 

2R + 15  = B + 5          sub (1)  in for  B

 

2R + 15  =  4R  + 5        subtract  5,  2R  from both sides

 

10  = 2R                     divide both sides by  2

 

5 = R  =   the  original number of red marbles

 

 

cool cool cool

 Jan 8, 2020

19 Online Users

avatar