document.write( "Question 97184: The smaller of two number is two-thirds of the larger, & the sum of their reciprocals is 1/6. What are the numbers? \n" ); document.write( "

Algebra.Com's Answer #70999 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The smaller of two numbers is two-thirds of the larger,
\n" ); document.write( "One number = x; smaller number = $\"%282x%29%2F3\"$
\n" ); document.write( ":
\n" ); document.write( "the sum of their reciprocals is 1/6. \r
\n" ); document.write( "\n" ); document.write( " $\"1%2Fx\"$ + $\"3%2F%282x%29\"$ = $\"1%2F6\"$
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\n" ); document.write( "What are the numbers?
\n" ); document.write( ":
\n" ); document.write( "The common denominator would be 6x, multiply equation by 6x
\n" ); document.write( "6x* $\"1%2Fx\"$ + 6x* $\"3%2F%282x%29\"$ = 6x* $\"1%2F6\"$
\n" ); document.write( ":
\n" ); document.write( "Cancel the denominators leaving:
\n" ); document.write( "6(1) + 3(3) = x(1)
\n" ); document.write( "6 + 9 = x
\n" ); document.write( "x = 15 is one number
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\n" ); document.write( "The smaller:
\n" ); document.write( " $\"2%2F3\"$ *15 = 10
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\n" ); document.write( "Check solution in original equation:
\n" ); document.write( " $\"1%2F15\"$ + $\"1%2F10%29\"$ = $\"1%2F6\"$
\n" ); document.write( " $\"2%2F30\"$ + $\"3%2F30%29\"$ = $\"5%2F30\"$ \n" ); document.write( "

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