document.write( "Question 135921: Where 3 times a certain number is added to twice its reciprocal the result is 5. What is the number \n" ); document.write( "

Algebra.Com's Answer #99586 by ptaylor(2198) $\"\"$ $\"About$

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Let x=the certain number\r
\n" ); document.write( "\n" ); document.write( "3x=3 times the certain number
\n" ); document.write( "The reciprocal of the certain number is 1/x
\n" ); document.write( "Twice the reciprocal is 2/x
\n" ); document.write( "Now we are told that:\r
\n" ); document.write( "\n" ); document.write( "3x+(2/x)=5 multiply each term by x\r
\n" ); document.write( "\n" ); document.write( "3x^2+2=5x subtract 5x from each side\r
\n" ); document.write( "\n" ); document.write( "3x^2-5x+2=0--------quadratic in standard form and it can be factored
\n" ); document.write( "(3x-2)(x-1)=0\r
\n" ); document.write( "\n" ); document.write( "3x-2=0
\n" ); document.write( "x=2/3
\n" ); document.write( "and
\n" ); document.write( "x-1=0
\n" ); document.write( "x=1\r
\n" ); document.write( "\n" ); document.write( "CK
\n" ); document.write( "3*(2/3)=2;
\n" ); document.write( "twice the reciprocal of 2/3 is 6/2 or 3
\n" ); document.write( "and 3+2=5 ok
\n" ); document.write( "Now
\n" ); document.write( "3*1=3
\n" ); document.write( "twice the reciprocal of 1 is 2
\n" ); document.write( "and 3+2=5 ok
\n" ); document.write( "SO, BOTH ANSWERS ARE GOOD!!\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor \n" ); document.write( "

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