document.write( "Question 567777: Suppose that the sum of two whole numbers is 20, and the sum of their reciprocals is 5/16. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #366688 by stanbon(75887) $\"\"$ $\"About$

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Suppose that the sum of two whole numbers is 20, and the sum of their reciprocals is 5/16. Find the numbers.
\n" ); document.write( "----------------------
\n" ); document.write( "Equations:
\n" ); document.write( "x + y = 20
\n" ); document.write( "1/x + 1/y = 5/16
\n" ); document.write( "-----------
\n" ); document.write( "x + y = 20
\n" ); document.write( "(x+y)/xy = 5/16
\n" ); document.write( "-----
\n" ); document.write( "20/xy = 5/16
\n" ); document.write( "5xy = 320
\n" ); document.write( "xy = 64
\n" ); document.write( "--
\n" ); document.write( "Remember x + y = 20
\n" ); document.write( "x = 20-y
\n" ); document.write( "---
\n" ); document.write( "Substitute:
\n" ); document.write( "(20-y)y = 64
\n" ); document.write( "20y-y^2 = 64
\n" ); document.write( "---------------
\n" ); document.write( "y^2-20y+64 = 0
\n" ); document.write( "y^2-16y-4y+64 = 0
\n" ); document.write( "y(y-16)-4(y-16) = 0
\n" ); document.write( "(y-16)(y-4) = 0
\n" ); document.write( "---
\n" ); document.write( "If y = 4; x = 16
\n" ); document.write( "If y = 16; x = 4
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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