document.write( "Question 1209492: Hi
\n" ); document.write( "The number of marbles in box A is half the number in box B. All the marbles in box A are black. Box B contains black and white marbles. In box B the number of black marbles is 3/4 the number of white marbles. There are 28 more black marbles in box A than in box B. What is the number of marbles in box A and box B \r
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Algebra.Com's Answer #848923 by ikleyn(52835) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "(a) The number of marbles in box A is half the number in box B.
\n" ); document.write( "(b) All the marbles in box A are black.
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\n" ); document.write( "(d) In box B the number of black marbles is 3/4 the number of white marbles.
\n" ); document.write( "(e) There are 28 more black marbles in box A than in box B.
\n" ); document.write( "What is the number of marbles in box A and box B
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\n" ); document.write( "\n" ); document.write( " I marked all conditions by letters for easy referring.\r
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document.write( "Let x be the number of all marbles in box A.  (They all are black.)\r\n" );
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document.write( "In box B we have 3y black marbles and 4y white marbles,\r\n" );
document.write( "   where y is some integer positive number (the common measure).\r\n" );
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document.write( "From condition (a), we have this equation\r\n" );
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document.write( "    2x = 3y + 4y,  or  2x = 7y.    (1)\r\n" );
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document.write( "From condition (e), we have this equation\r\n" );
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document.write( "    x - 3y = 28.                   (2)\r\n" );
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document.write( "To solve, from equation (2) express x = 28 + 3y  and substitute it into equation (1).  You will get\r\n" );
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document.write( "    2(28+3y) = 7y.\r\n" );
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document.write( "Simplify and find y\r\n" );
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document.write( "    56 + 6y = 7y\r\n" );
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document.write( "    56 = 7y - 6y.\r\n" );
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document.write( "    56 = y.\r\n" );
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document.write( "So, the number of all marbles in box B is 7y = 7*56 = 392.\r\n" );
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document.write( "    The number of all marbles in box A is half of that, i.e.  392/2 = 196.\r\n" );
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document.write( "From the problem's question, I can not get, if they want the total number of marbles or separate numbers.\r\n" );
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document.write( "In my view, the question is worded in extremely illiterate/inaccurate  form; \r\n" );
document.write( "in the true Math problems, professional composers NEVER write it in this way.\r\n" );
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document.write( "True question must ask either \r\n" );
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document.write( "    \"What is the number of marbles in box A and box B separately ?\"\r\n" );
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document.write( "or\r\n" );
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document.write( "    \"What is the total number of marbles in box A and box B ?\".\r\n" );
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document.write( "But as I see it in many incoming posts, the major goal of the local problem composers\r\n" );
document.write( "is to confuse a reader.\r\n" );
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document.write( "If you need the total, then add 392 and 196:  392 + 196 = 588.\r\n" );
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