Algebra

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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 -

    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 -

    how did you get a positive 6

  • Algebra -

    In your question, didn't it say that 6 yellow marbles were added ????

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