document.write( "Question 1114107: Find the missing number\r\n" );
document.write( "27 74 215\r\n" );
document.write( "12 x 80\r\n" );
document.write( "39 110 323
\n" );
document.write( "
Algebra.Com's Answer #754777 by Edwin McCravy(20060)![]() ![]() You can put this solution on YOUR website! Find the missing number\r\n" ); document.write( "27 74 215\r\n" ); document.write( "12 x 80\r\n" ); document.write( "39 110 323\r\n" ); document.write( "\r\n" ); document.write( "We notice on the top row that\r\n" ); document.write( "if we divide 74 by 27 we get 2.74...\r\n" ); document.write( "and if we divide 215 by 74 we get 2.905...\r\n" ); document.write( "\r\n" ); document.write( "We notice on the bottom row that\r\n" ); document.write( "if we divide 110 by 39 we get 2.82...\r\n" ); document.write( "and if we divide 323 by 110 we get 2.936...\r\n" ); document.write( "\r\n" ); document.write( "We notice that these are all close to 3.\r\n" ); document.write( "So the 1st and 3rd rows are close to a geometric sequence with common ratio 3.\r\n" ); document.write( "So we check to see how much less than multiplying by 3 each next number is.\r\n" ); document.write( "\r\n" ); document.write( "For the 1st row, \r\n" ); document.write( "27×3=81 we find that we must subtract 7 to get the next number, 74.\r\n" ); document.write( "74×3=222 we find that we must subtract 7 to get the next number, 215.\r\n" ); document.write( "\r\n" ); document.write( "For the 3rd row, \r\n" ); document.write( "39×3=117 we find that we must subtract 7 to get the next number, 110.\r\n" ); document.write( "110×3=330 we find that we must subtract 7 to get the next number, 323.\r\n" ); document.write( "\r\n" ); document.write( "So that makes us wonder if the 2nd row is like the other two.\r\n" ); document.write( "\r\n" ); document.write( "If so then x would be 12×3=36 minus 7 or 29.\r\n" ); document.write( "\r\n" ); document.write( "As a final check, we see what 29×3=87 minus 7 is, and hooray, it's 80.\r\n" ); document.write( "\r\n" ); document.write( "Whoopedoo, so x=29 \r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |