document.write( "Question 714706: one third of the result obtained by adding 5 to a certain numnber is equal to one-half of the result obtained when 5 is subtracted from the number. Find the number \n" ); document.write( "

Algebra.Com's Answer #438979 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
a certain number = x
\n" ); document.write( "add 5 to a certain number = (x+5)
\n" ); document.write( "one third of (add 5 to a certain number) = (1/3)(x+5)
\n" ); document.write( "5 subtracted from a the certain number = (x-5)
\n" ); document.write( "one half of (5 subtracted from a the certain number) = (1/2)(x-5)

\n" ); document.write( "So \"one third of the result obtained by adding 5 to a certain numnber is equal to one-half of the result obtained when 5 is subtracted from the number\" translates into:
\n" ); document.write( " $\"%281%2F3%29%28x%2B5%29+=+%281%2F2%29%28x-5%29\"$

\n" ); document.write( "Now we solve for x. We could start by multiplying out each side but that will involve a lot of fractions. Instead we'll eliminate the the fractions by multiplying both sides of the equation by the lowest common denominator (LCD) of the two denominators. The LCD of 3 and 2 is 6.
\n" ); document.write( " $\"6%28%281%2F3%29%28x%2B5%29%29+=+6%28%281%2F2%29%28x-5%29%29\"$
\n" ); document.write( "which simplifies as follows:
\n" ); document.write( " $\"2%28x%2B5%29+=+3%28x-5%29\"$
\n" ); document.write( " $\"2x%2B10+=+3x-15\"$
\n" ); document.write( "With the fractions gone the rest is easy. Subtractin 2x from each side:
\n" ); document.write( " $\"10+=+x+-+15\"$
\n" ); document.write( "Adding 15 to each side:
\n" ); document.write( " $\"25+=+x\"$ \n" ); document.write( "

\n" );