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a four-digit positive integer such that the sum of my digits is 18 and my digits
\n" ); document.write( " reversed are exactly four times greater than myself. What number am I?
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\n" ); document.write( "We know the 1st digit has to be 1 or 2, (multiplying any other number by 4
\n" ); document.write( "would give us a 5 digit number)
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\n" ); document.write( "Assuming it's 2, then the last number would be 8 (4*2=8)
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\n" ); document.write( "let the middle digits be x & y:
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\n" ); document.write( "2 + x + y + 8 = 18
\n" ); document.write( "x + y = 18 - 10
\n" ); document.write( "x + y = 8
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\n" ); document.write( "2000 + 100x + 10y + 8 = the number
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\n" ); document.write( "\"digits reversed are exactly four times greater than myself.
\n" ); document.write( "4(2000 + 100x + 10y + 8) = 8000 + 100y + 10x + 2
\n" ); document.write( " 8000 + 400x + 40y + 32 = 8000 + 100y + 10x + 2
\n" ); document.write( " 400x + 40y + 8032 = 100y + 10x + 8002
\n" ); document.write( "400x - 10x + 40y - 100y = 8002 - 8032
\n" ); document.write( "390x - 60y = - 30
\n" ); document.write( "Simplify, divide by 10
\n" ); document.write( "39x - 6y = -3
\n" ); document.write( "Multiply the 1st equation by 6 and add
\n" ); document.write( "39x - 6y = -3
\n" ); document.write( " 6x + 6y = 48
\n" ); document.write( "-------------- adding eliminates y
\n" ); document.write( "45x = 45
\n" ); document.write( "x = 1 is the 2nd digit
\n" ); document.write( "then, obviously
\n" ); document.write( "y = 7 is the 3rd digit
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\n" ); document.write( "2178 is the number
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\n" ); document.write( "4 * 2178 = 8712; sorry about that!! \n" ); document.write( "