Question 296183: Alphonse has three times as many marbles as Beatrice. If Alphonse would give 15 of his marbles to Beatrice then he would have twice as many marbles as she does. How many marbles must Alphonse give to Beatrice so that they each have the same number?
(A) 30 (B) 45 (C) 60 (D) 90 (E) Not enough Information
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! let beatrice have x marbles
Al will have 3x
3x-15 = 2* x
3x-2x=15
x=15
beatrice has 15 marbles
Alphonse has 45 marbles
15+45 / 2 = 30
So alphonse must give 15 marbles to beatrice so that they have the same number 30 marbles
Answer by ikleyn(53875)  (Show Source):
You can put this solution on YOUR website! .
Alphonse has three times as many marbles as Beatrice. If Alphonse would give 15 of his marbles to Beatrice
then he would have twice as many marbles as she does. How many marbles must Alphonse give to Beatrice
so that they each have the same number?
(A) 30 (B) 45 (C) 60 (D) 90 (E) Not enough Information
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The solution in the post by @mananth is incorrect, because his setup equation is wrong.
I came to bring a correct solution.
Let's Beatrice has x marbles.
Then Alphonse has 3x marbles.
After giving, Alphonse has (3x-15) marbles; Beatrice has (x+15) marbles.
The setup equation is
3x - 15 = 2(x+15).
Simplify and find x
3x - 15 = 2x + 30,
3x - 2x = 30 + 15,
x = 45.
Thus, initially Beatrice has 45 marbles, Alphonse has 3*45 = 135 marbles.
Let 'y' be the number of marbles Alphonse should give to Beatrice so they each has the same number
135 - y = 45 + y,
135 - 45 = y + y,
90 = 2y,
y = 90/2 = 45.
ANSWER. Alphonse should give 45 marbles to Beatrice so they each has the same number of marbles.
Solved correctly.
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