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# help

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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
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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   Jan 8, 2020