document.write( "Question 1025104: one number is 10 more than the 1/3 of the second number find the numbers for which the product is a minimum then find the minimum product \n" ); document.write( "

Algebra.Com's Answer #640413 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the numbers be $\"+x+\"$ and $\"+y+\"$
\n" ); document.write( " $\"+x+=+%281%2F3%29%2Ay+%2B+10+\"$
\n" ); document.write( "The product is:
\n" ); document.write( " $\"+x%2Ay+\"$
\n" ); document.write( " $\"+%281%2F3%29%2Ay+%2B+10+=+x+\"$
\n" ); document.write( " $\"+%281%2F3%29%2Ay+=+x+-+10+\"$
\n" ); document.write( " $\"+y+=+3x+-+30+\"$
\n" ); document.write( "----------------
\n" ); document.write( " $\"+x%2Ay+=+x%2A%28+3x+-+30+%29+\"$
\n" ); document.write( " $\"+x%2Ay+=+3x%5E2+-+30x+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "The formula for minimum is:
\n" ); document.write( " $\"+x%5Bmin%5D+=+-b%2F%282a%29+\"$
\n" ); document.write( " $\"+x%5Bmin%5D+=+-%28-30%29+%2F+%28+2%2A3+%29+\"$
\n" ); document.write( " $\"+x%5Bmin%5D+=+5+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+y+=+3x+-+30+\"$
\n" ); document.write( " $\"+y+=+-15+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "When the numbers are 5 and -15, the product is a minimum
\n" ); document.write( "The minimum product is $\"+5%2A%28-15%29+=+-75+\"$
\n" ); document.write( "------------------
\n" ); document.write( "check:
\n" ); document.write( "Suppose $\"+x+=+5.1+\"$
\n" ); document.write( " $\"+y+=+3x+-+30+\"$
\n" ); document.write( " $\"+y+=+15.3+-+30+\"$
\n" ); document.write( " $\"+y+=+-14.7+\"$
\n" ); document.write( " $\"+x%2Ay+=+5.1%2A14.7+\"$
\n" ); document.write( " $\"+x%2Ay+=+-74.97+\"$
\n" ); document.write( "This is larger than $\"+-75+\"$ , so
\n" ); document.write( " $\"+5%2A%28-15%29+\"$ seems to be the minimum \n" ); document.write( "

\n" );