document.write( "Question 158188: I'm struggling on 2 algebra problems I have. If you could please help me I would greatly appreaciate it.\r
\n" ); document.write( "\n" ); document.write( "1) The sum of two numbers is 43. One number plus three times the other number is 65. What are the numbers?\r
\n" ); document.write( "\n" ); document.write( " x + x = 43\r
\n" ); document.write( "\n" ); document.write( " x + 3x = 65\r
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\n" ); document.write( "\n" ); document.write( "2) The difference between two numbers is 55. Four times the smaller number plus five times the larger number is 176. What are the numbers?\r
\n" ); document.write( "\n" ); document.write( " z = smaller number \r
\n" ); document.write( "\n" ); document.write( " y = larger number\r
\n" ); document.write( "\n" ); document.write( " x - x = 55\r
\n" ); document.write( "\n" ); document.write( " 4z + 5y = 76\r
\n" ); document.write( "\n" ); document.write( "
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Algebra.Com's Answer #116562 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Edwin's explanation of your error:
\n" ); document.write( "I'm struggling on 2 algebra problems I have. If you could please help me I would greatly appreaciate it.
\n" ); document.write( "1) The sum of two numbers is 43. One number plus three times the other number is 65. What are the numbers?
\n" ); document.write( "x + x = 43
\n" ); document.write( "x + 3x = 65
\n" ); document.write( "
\r\n" );
document.write( "I'm afraid that's wrong. Your mistake is trying to use the SAME\r\n" );
document.write( "letter x for two DIFFERENT numbers.  You must use DIFFERENT \r\n" );
document.write( "letters for DIFFERENT numbers.\r\n" );
document.write( "\r\n" );
document.write( "First number = \"x\"\r\n" );
document.write( "Second number = \"y\"\r\n" );
document.write( "\r\n" );
document.write( "\"system%28x+%2B+y+=+43%2C+x+%2B+3y+=+65%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve the first equation for \"x\"\r\n" );
document.write( "\"x%2By=43\"\r\n" );
document.write( "\"x=43-y\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute \"%2843-y%29\" for \"x\" is the second equation,\r\n" );
document.write( "then solve for \"y\"\r\n" );
document.write( "\r\n" );
document.write( "\"x+%2B+3y+=+65\"\r\n" );
document.write( "\"%2843-y%29+%2B+3y+=+65\"\r\n" );
document.write( "\"43-y+%2B+3y+=+65\"\r\n" );
document.write( "\"43%2B+2y+=+65\"\r\n" );
document.write( "\"2y+=+65-43\"\r\n" );
document.write( "\"2y=22\"\r\n" );
document.write( "\"y=11\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute \"11\" for \"y\" in \"x=43-y\"\r\n" );
document.write( "\r\n" );
document.write( "\"x=43-y\"\r\n" );
document.write( "\"x=43-11\"\r\n" );
document.write( "\"x=32\"  \r\n" );
document.write( "\r\n" );
document.write( "------------------------\r\n" );
document.write( "

\n" ); document.write( "2) The difference between two numbers is 55. Four times the smaller number plus five times the larger number is 176. What are the numbers?
\n" ); document.write( "z = smaller number
\n" ); document.write( "y = larger number
\n" ); document.write( "x - x = 55
\n" ); document.write( "4z + 5y = 176
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Hmm! Now your equation \"4z%2B5y=76\" is OK, but your first \r\n" );
document.write( "equation should not have involved \"x\" at all, but \"z\" \r\n" );
document.write( "and \"y\" only.  And again, on top of that, your mistake \r\n" );
document.write( "was using the SAME letter \"x\" for two DIFFERENT quantities.  \r\n" );
document.write( "You must use DIFFERENT letters for DIFFERENT quantities, never \r\n" );
document.write( "the SAME letter. Your first equation should have been \r\n" );
document.write( "\"LARGER-SMALLER=y-z=55\"\r\n" );
document.write( "\r\n" );
document.write( "So you have this system:\r\n" );
document.write( "\r\n" );
document.write( "\"system%28y+-+z+=+55%2C+4z+%2B+5y+=+176%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve the first equation for \"y\"\r\n" );
document.write( "\"y-z=55\"\r\n" );
document.write( "\"y=55%2Bz\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute \"%2855%2Bz%29\" for \"y\" is the second equation,\r\n" );
document.write( "then solve for \"z\"\r\n" );
document.write( "\r\n" );
document.write( "\"4z+%2B+5y+=+176\"\r\n" );
document.write( "\"4z+%2B+5%2855%2Bz%29+=+176\"\r\n" );
document.write( "\"4z+%2B+275%2B5z+=+176\"\r\n" );
document.write( "\"9z+%2B+275+=+176\"\r\n" );
document.write( "\"9z+=+176-275\"\r\n" );
document.write( "\"9z=-99\"\r\n" );
document.write( "\"z=-11\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute \"-11\" for \"z\" in \"y=55%2Bz\"\r\n" );
document.write( "\r\n" );
document.write( "\"y=55%2Bz\"\r\n" );
document.write( "\"y=55%2B%28-11%29\"\r\n" );
document.write( "\"y=44\" \r\n" );
document.write( "\r\n" );
document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com\r\n" );
document.write( "
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