document.write( "Question 1163137: A box contained 50Cents coins and 20 cents coins in the ratio 2:3.when I took out foor 50Cents coins, exchanged them for 20 cents coins. And then put the money back in the box, the ratio became 2:7. Find the sum of money in the box. \n" ); document.write( "

Algebra.Com's Answer #787165 by ikleyn(52946) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            If you take a labor to solve the system of equations, which @josgarithmetic prepared for you in his post,\r
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\n" ); document.write( "\n" ); document.write( "            you will discover at the end that the system HAS NO integer solution.\r
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\n" ); document.write( "\n" ); document.write( "            If so, it means that something is going wrong.\r
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\n" ); document.write( "\n" ); document.write( "            So, I read the problem attentively, and I came to the conclusion that the problem should be read and interpreted DIFFERENTLY.\r
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\n" ); document.write( "\n" ); document.write( "            Below is my interpretation and the full solution.\r
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document.write( "According to the condition, we can assume that initially there were 2x of the 50-cent coins and 3x of the 20-cent coins in the box.\r\n" );
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document.write( "When 4 of the 50-cent coins were taken out, the number of the 50-cent coins became (2x-4).\r\n" );
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document.write( "When these 4 50-cent coins were exchanged for 20-cent coins, 10 of 20-cent coins were returned to the box,\r\n" );
document.write( "making the number of the 20-cent coins in the box equal to (3x+10).\r\n" );
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document.write( "So, your proportion is now\r\n" );
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document.write( "     = .\r\n" );
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document.write( "From the proportion,\r\n" );
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document.write( "    7*(2x-4) = 2*(3x+10)\r\n" );
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document.write( "    14x - 28 = 6x + 20\r\n" );
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document.write( "    14x - 6x = 20 + 28\r\n" );
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document.write( "     8x      = 48\r\n" );
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document.write( "      x      = 48/8 = 6.\r\n" );
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document.write( "So, initially in the box there were  2*6 = 12 of the 50-cent coins  and  \r\n" );
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document.write( "                                     3*6 = 18 of the 20-cent coins.\r\n" );
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document.write( "Therefore, the total money in the box was  12*50 + 18*20 = 960 cents,  or  9.60 dollars.     ANSWER\r\n" );
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