Posted by **Mingma Sherpa** on Thursday, May 5, 2011 at 6:48pm.

A sack contains yellow marbles and black marbles. If one marble is drawn at random, the probability that it is yellow is 7/8. Six yellow marbles are added to the sack. Now, if one marble is drawn, the probability that it is yellow is 9/10. How many yellow and black marbles were initially in the sack?

- Algebra -
**Reiny**, Thursday, May 5, 2011 at 7:30pm
original bag

yellow marbles -- y

black marbles --b

so y/(y+b) = 7/8

8y = 7y + 7b

y = 7b

new bag:

yellow marbles -- y+6

black marbles --- b

(y+6)/(y+6+b) = 9/10

10y+60 = 9y+54+9b

y = 9b - 6

then 9b-6 = 7b

2b=6

b = 3

then y = 7(3) or 21

so there were 21 yellow and 3 black

for a total of 24 marbles

check:

Prob(yellow) = 21/24 = 7/8

new bag:

27 yellow, still 3 black, total 30

prob(yellow) = 27/30 = 9/10

- Algebra -
**Mingma Sherpa**, Thursday, May 5, 2011 at 7:55pm
how did you get a positive 6

- Algebra -
**Reiny**, Thursday, May 5, 2011 at 9:28pm
In your question, didn't it say that 6 yellow marbles were added ????

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