document.write( "Question 1189278: A jar contains red, white, and yellow candy pieces
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\n" ); document.write( "candy and 5 pieces of white candy are removed
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\n" ); document.write( "the ratio of red to white to yellow becomes 4: 2: 3.
\n" ); document.write( "If the jar contains only these three colors of candy,
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Algebra.Com's Answer #820592 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A jar contains red, white, and yellow candy pieces
\n" ); document.write( "in the ratio 9:5:4 of respectively. When 7 pieces of red
\n" ); document.write( "candy and 5 pieces of white candy are removed
\n" ); document.write( "from the jar and 3 pieces of yellow candy are added,
\n" ); document.write( "the ratio of red to white to yellow becomes 4: 2: 3.
\n" ); document.write( "If the jar contains only these three colors of candy,
\n" ); document.write( "how many pieces were originally in the jar?
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document.write( "From the condition, we can write\r\n" );
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document.write( "    R = 9x,  W = 5x,  Y = 4x\r\n" );
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document.write( "for the number of red, white and yellow candy pieces in the jar originally,\r\n" );
document.write( "where x is the common factor (multiplier).\r\n" );
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document.write( "According to the condition, we have this proportion\r\n" );
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document.write( "     =  = 2,\r\n" );
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document.write( "which gives\r\n" );
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document.write( "    9x - 7 = 2*(5x-5)\r\n" );
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document.write( "    9x - 7 = 10x - 10\r\n" );
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document.write( "    10 - 7 = 10x - 9x\r\n" );
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document.write( "       x = 3.\r\n" );
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document.write( "At this point, we can just answer the problem's question: R = 27,  W = 15,  Y = 12.\r\n" );
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document.write( "The last condition is EXCESSIVE, and we should check that it does not contradict to \r\n" );
document.write( "(is consistent with) the answer.\r\n" );
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document.write( "CHECK.  After manipulations, the jar contains  R = 20,  W = 10  and Y = 15 candy pieces,\r\n" );
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document.write( "       so this proportionality  4 : 2 : 3  is held for the final state.\r\n" );
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