document.write( "Question 1155803: The sum of 39 consecutive number is 1170, what is the largest of these 39 number could be? \n" ); document.write( "
Algebra.Com's Answer #778466 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Let \"+a+%2B+1+\" be the first of the 39 consecutive numbers
\n" ); document.write( "\"+a+%2B+39+\" is the 39th of the consecutive numbers
\n" ); document.write( "1 through \"+a+\" are the \"+a+\" numbers preceding the 39
\n" ); document.write( "consecutive numbers
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\n" ); document.write( "The sum of the \"+39+%2B+a+\" numbers is:
\n" ); document.write( "\"+%28+39+%2B+a+%29%2A%28+40+%2B+a+%29+%2F+2+\"
\n" ); document.write( "The sum of the 1 through \"+a+\" numbers is:
\n" ); document.write( "\"+a%2A%28+a+%2B+1+%29+%2F+2+\"
\n" ); document.write( "Let the sum of the 39 consecutive numbers be \"+S+\"
\n" ); document.write( "\"+S+=++%28+39+%2B+a+%29%2A%28+40+%2B+a+%29+%2F+2+-++a%2A%28+a+%2B+1+%29+%2F+2+\"
\n" ); document.write( "\"+2S+=+1560+%2B+40a+%2B+39a+%2B+a%5E2+-+a%5E2+-+a+\"
\n" ); document.write( "\"+2S+=+78a+%2B+1560+\"
\n" ); document.write( "\"+S+=+39a+%2B+780+\"
\n" ); document.write( "\"+1170+=+39a+%2B+780+\"
\n" ); document.write( "\"+39a+=+390+\"
\n" ); document.write( "\"+a+=+10+\"
\n" ); document.write( "and
\n" ); document.write( "\"+a+%2B+1+=+11+\"
\n" ); document.write( "\"+11+%2B+38+=+49+\"
\n" ); document.write( "49 is the largest number
\n" ); document.write( "------------------------------
\n" ); document.write( "check:
\n" ); document.write( "\"+S+=++%28+39+%2B+a+%29%2A%28+40+%2B+a+%29+%2F+2+-++a%2A%28+a+%2B+1+%29+%2F+2+\"
\n" ); document.write( "\"+S+=++%28+39+%2B+10+%29%2A%28+40+%2B+10+%29+%2F+2+-++10%2A%28+10+%2B+1+%29+%2F+2+\"
\n" ); document.write( "\"+S+=+%2849%2A50%29%2F2+-+%2810%2A11%29%2F2+\"
\n" ); document.write( "\"+S+=+2450%2F2+-+110%2F2+\"
\n" ); document.write( "\"+S+=+1225+-+55+\"
\n" ); document.write( "\"+S+=+1170+\"
\n" ); document.write( "OK
\n" ); document.write( "Definitely get a 2nd opinion if needed
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