document.write( "Question 826722: Find two numbers such that the sum of the first and three times the second is 5 and the sum of the second and two times the first is 8. \n" ); document.write( "

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Find two numbers such that the sum of the first and three times the second is 5 and the sum of the second and two times the first is 8.
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "Find two numbers such that the sum of the first and three times the second is 5 and the sum of the second and two times the first is 8.\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "Define the variables:\r\n" );
document.write( "Let x be the first number.\r\n" );
document.write( "Let y be the second number.\r\n" );
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document.write( "Write two equations modeling the relationships in the problem.\r\n" );
document.write( "The sum of the first and three times the second is 5.\r\n" );
document.write( "\"The first\" is x, and \"three times the second\" is 3y.\r\n" );
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document.write( "Their sum is 5, so one equation is x + 3y = 5.\r\n" );
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document.write( "For the other equation,\r\n" );
document.write( "The sum of the second and two times the first is 8.\r\n" );
document.write( "\"The second\" is y, and \"two times the first\" is 2x.\r\n" );
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document.write( "The sum is 8, so another equation is y + 2x = 8.\r\n" );
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document.write( "Solve the System of Equations:\r\n" );
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document.write( "x + 3y = 5\r\n" );
document.write( "y + 2x = 8\r\n" );
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document.write( "Rewrite the first equation in \"x=\" form.\r\n" );
document.write( "x + 3y = 5\r\n" );
document.write( "x = -3y + 5\r\n" );
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document.write( "Substitute -3y+5 for x in the second equation equation. Simplify and solve for y.\r\n" );
document.write( "y + 2x = 8 = 8\r\n" );
document.write( "y + 2(-3y + 5) = 8\r\n" );
document.write( "y - 6y + 10 = 8\r\n" );
document.write( "-5y + 10 = 8\r\n" );
document.write( "-5y = -2\r\n" );
document.write( "y = 2/5\r\n" );
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document.write( "The second number is 2/5.\r\n" );
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document.write( "Solve for x using the first equation.\r\n" );
document.write( "x + 3y = 5\r\n" );
document.write( "x + 3(2/5) = 5\r\n" );
document.write( "x + 6/5 = 5\r\n" );
document.write( "x = 5 - 6/5\r\n" );
document.write( "x = 25/5 - 6/5\r\n" );
document.write( "x = 19/5\r\n" );
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document.write( "The first number is 19/5.\r\n" );
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document.write( "NOW CHECK your work with the original sentences:\r\n" );
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document.write( "The sum of the first and three times the second is 5.\r\n" );
document.write( "(19/5) + 3*(2/5) = 5\r\n" );
document.write( "19/5 + 6/5 = 5\r\n" );
document.write( "25/5 = 5\r\n" );
document.write( "5 = 5 CHECK!\r\n" );
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document.write( "The sum of the second and two times the first is 8.\r\n" );
document.write( "(2/5) + 2*(19/5) = 8\r\n" );
document.write( "2/5 + 38/5 = 8\r\n" );
document.write( "40/5 = 8\r\n" );
document.write( "8 = 8 CHECK!\r\n" );
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document.write( "The two numbers are 2/5 and 19/5.\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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