document.write( "Question 214070: Find the six-digit number in which the first digit is one less than the second digit and half the third; the fourth digit is one more than the third and is also the sum of the first and second digits; and the fifth and sixth digits make a number that is the sum of the first four digits. The sum of all the digits is 19. \n" ); document.write( "
Algebra.Com's Answer #161746 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Write an equation for each statement
\n" ); document.write( ":
\n" ); document.write( "Find the six-digit number
\n" ); document.write( "u, v, w, x, y, z
\n" ); document.write( ":
\n" ); document.write( " in which the first digit is one less than the second digit
\n" ); document.write( "u = v-1
\n" ); document.write( ":
\n" ); document.write( " and half the third;
\n" ); document.write( "u = .5w
\n" ); document.write( ":
\n" ); document.write( " the fourth digit is one more than the third
\n" ); document.write( "x = w+1
\n" ); document.write( ":
\n" ); document.write( " and is also the sum of the first and second digits;
\n" ); document.write( "x = u + v
\n" ); document.write( ":
\n" ); document.write( "the fifth and sixth digits make a number that is the sum of the first four digits.
\n" ); document.write( "10y + z = u + v + w + x
\n" ); document.write( ":
\n" ); document.write( " The sum of all the digits is 19.
\n" ); document.write( "u + v + w + x + y + z = 19
\n" ); document.write( ":
\n" ); document.write( "We can replace the 1st 4 digits with 10y + z
\n" ); document.write( "10y + z + y + z = 19
\n" ); document.write( "11y + 2z = 19
\n" ); document.write( ":
\n" ); document.write( "From this we can write an equation that has only one positive integer solution
\n" ); document.write( "2z = 19-11y
\n" ); document.write( "z = \"%2819-11y%29%2F2\"
\n" ); document.write( "y = 1
\n" ); document.write( "z = \"%2819-11%29%2F2\"
\n" ); document.write( "z = \"8%2F2\"
\n" ); document.write( "z = 4
\n" ); document.write( ":
\n" ); document.write( "u + v + w + x + y + z = 19
\n" ); document.write( "Replace y and z
\n" ); document.write( "u + v + w + x + 1 + 4 = 19
\n" ); document.write( "u + v + w + x = 19 - 5
\n" ); document.write( "u + v + w + x = 14
\n" ); document.write( ":
\n" ); document.write( "Replace u with .5w, replace x with w+1
\n" ); document.write( ".5w + v + w + (w+1) = 14
\n" ); document.write( "2.5w + v = 14 - 1
\n" ); document.write( "2.5w + v = 13
\n" ); document.write( ":
\n" ); document.write( "We know that u = v-1 and we know that u = .5w, therefore
\n" ); document.write( ".5w = v - 1
\n" ); document.write( "or
\n" ); document.write( "v = .5w + 1
\n" ); document.write( "Replace v with (.5w+1)
\n" ); document.write( "2.5w + .5w + 1 = 13
\n" ); document.write( "3w = 13 - 1
\n" ); document.write( "3w = 12
\n" ); document.write( "w = 4
\n" ); document.write( ":
\n" ); document.write( "Find v
\n" ); document.write( "v = .5(4) + 1
\n" ); document.write( "v = 3
\n" ); document.write( ":
\n" ); document.write( "So far we have:
\n" ); document.write( "v=3, w=4, y=1, z=4
\n" ); document.write( "find x
\n" ); document.write( "x = w+1
\n" ); document.write( "x = 4+1
\n" ); document.write( "x = 5
\n" ); document.write( ":
\n" ); document.write( "find u
\n" ); document.write( "u = .5w
\n" ); document.write( "u = .5(4)
\n" ); document.write( "u = 2
\n" ); document.write( ":
\n" ); document.write( "The number: 234514
\n" ); document.write( ":
\n" ); document.write( "Check this:
\n" ); document.write( "2 + 3 + 4 + 5 + 1 + 4 = 19\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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