document.write( "Question 1071619: The sum of 4 times the first number and 10 times the second number is 48. The sum of 10 times the first number and 4 times the second number is 36. What are the two numbers?
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Algebra.Com's Answer #686505 by math_helper(2461) $\"\"$ $\"About$

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document.write( "4x+10y = 48  (1)\r\n" );
document.write( "10x+4y = 36  (2)\r\n" );
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document.write( "Multiply both sides of (1) by 10, and both sides of (2) by 4:\r\n" );
document.write( "40x + 100y = 480   (1')\r\n" );
document.write( "40x + 16y   = 144   (2')\r\n" );
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document.write( "Subtract (2') from (1') to get:\r\n" );
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document.write( "  0x + 84y = 336   —>   y = 336/84 = 4.   \r\n" );
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document.write( " Using 4x + 10y = 48 and y=4  —>  4x + 10(4) = 48 —>  4x = 48-40 —> 4x = 8 —> x=2\r\n" );
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document.write( "Ans:   and \r\n" );
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document.write( "Check:   4(2) + 10(4) = 8 + 40 = 48   (ok, eqn 1 works)\r\n" );
document.write( "         10(2) + 4(4) = 20 + 16 = 36  (ok, eqn 2 works as well)\r\n" );
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