A, B and C have 100, x and y marbles respectively. If B gives 20 marbles to A, he is left with half
as many as C. If together they had 60 more marbles, each of them would have had 100 marbles
on an average. Find x:y.
Answers
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If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?
A) 5
B) 9
C) 12
D) 23
E) 46
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We are given a table with the following information:
Bag P has 37 marbles and 10.8% of those marbles are blue. So there are 0.108(37) = 3.996, or 4, blue marbles in bag P.
Bag Q has X marble and 66.7% of those marbles are blue. Recall that the fraction 2/3 is approximately 66.7%, so there are (2/3)X blue marbles in bag Q.
Bag R has 32 marbles and 50% of those marbles are blue. So, there are 0.5(32) = 16 blue marbles in bag R.
We are also given that 1/3 of the total marbles in the 3 bags are blue. Thus, we can create the following equation:
1/3(37 + X + 32) = 4 + (2/3)X + 16
Multiplying the equation by 3, we have:
37 + X + 32 = 12 + 2X + 48
X + 69 = 2X + 60
X = 9
There are 9 marbles in bag Q.
Answer: B