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Write an equation for each statement
\n" ); document.write( ":
\n" ); document.write( "A number consist of three digits
\n" ); document.write( "a, b, c
\n" ); document.write( "100a + 10b + c = \"the number\"
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\n" ); document.write( " of whose sum is 17
\n" ); document.write( "a + b + c = 17
\n" ); document.write( ":
\n" ); document.write( " the middle digit exceeds the sum of two digits by one
\n" ); document.write( "b = a + c + 1
\n" ); document.write( "It's easy to find b now, rearrange the above and add to the first equation
\n" ); document.write( "a + b + c = 17
\n" ); document.write( "-a +b - c = 1
\n" ); document.write( "---------------Adding eliminates a and c, find b
\n" ); document.write( "2b = 18
\n" ); document.write( "b = 9
\n" ); document.write( ":
\n" ); document.write( "if the digits of the number are reversed the number diminishes by 396
\n" ); document.write( "100a + 10b + c - (100c + 10b + a) = 396
\n" ); document.write( "100a + 10b + c - 100c - 10b - a = 396
\n" ); document.write( "Combine like terms
\n" ); document.write( "100a - a + 10b - 10b + c - 100c = 396
\n" ); document.write( "99a - 99c = 396
\n" ); document.write( "Simplify, divide by 99
\n" ); document.write( "a - c = 4
\n" ); document.write( "a = (c+4)
\n" ); document.write( ":
\n" ); document.write( "Find the number
\n" ); document.write( ":
\n" ); document.write( "Using the 1st equation: a + b + c = 17, replace a and b
\n" ); document.write( "(c+4) + 9 + c = 17
\n" ); document.write( "2c + 13 = 17
\n" ); document.write( "2c = 17-13
\n" ); document.write( "2c = 4
\n" ); document.write( "c = 2
\n" ); document.write( "then
\n" ); document.write( "a = c + 4
\n" ); document.write( "a = 2 + 4
\n" ); document.write( "a = 6
\n" ); document.write( ":
\n" ); document.write( "692 is the number
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\n" ); document.write( "Check this 692 - 296 = 396 \n" ); document.write( "