document.write( "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?\r
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Algebra.Com's Answer #854269 by ikleyn(53875) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Alphonse has three times as many marbles as Beatrice. If Alphonse would give 15 of his marbles to Beatrice
\n" ); document.write( "then he would have twice as many marbles as she does. How many marbles must Alphonse give to Beatrice
\n" ); document.write( "so that they each have the same number?
\n" ); document.write( "(A) 30 (B) 45 (C) 60 (D) 90 (E) Not enough Information
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\n" ); document.write( "\n" ); document.write( " The solution in the post by @mananth is incorrect, because his setup equation is wrong.
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document.write( "Let's Beatrice has x marbles.\r\n" );
document.write( "Then Alphonse has 3x marbles.\r\n" );
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document.write( "After giving, Alphonse has  (3x-15) marbles;  Beatrice has (x+15) marbles.\r\n" );
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document.write( "The setup equation is\r\n" );
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document.write( "    3x - 15 = 2(x+15).\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    3x - 15 = 2x + 30,\r\n" );
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document.write( "    3x - 2x = 30 + 15,\r\n" );
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document.write( "       x    =    45.\r\n" );
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document.write( "Thus, initially Beatrice has 45 marbles, Alphonse has 3*45 = 135 marbles.\r\n" );
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document.write( "Let 'y' be the number of marbles Alphonse should give to Beatrice so they each has the same number\r\n" );
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document.write( "    135 - y = 45 + y,\r\n" );
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document.write( "    135 - 45 = y + y,\r\n" );
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document.write( "        90   =  2y,\r\n" );
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document.write( "         y   =  90/2 = 45.\r\n" );
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document.write( "ANSWER.  Alphonse should give 45 marbles to Beatrice so they each has the same number of marbles.\r\n" );
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