document.write( "Question 137560: The some of a digit is 8. If 18 is added to the number , the digits of the new numeral are those of the original numeral, but they appear in reversed order.\r
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\n" ); document.write( "\n" ); document.write( "The some of the digits is 8. The number 16 is less than the product of 3 and the number represented when the digits are interchanged. \n" ); document.write( "
Algebra.Com's Answer #100633 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
I rewrote both problems slightly.
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\n" ); document.write( "The sum of the digits is 8. If 18 is added to the number , the digits of the new numeral are those of the original numeral, but they appear in reversed order.
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\n" ); document.write( "Let x = 10's digit of the original number
\n" ); document.write( "Let y = units digit of the original number
\n" ); document.write( "The number = 10x + y
\n" ); document.write( ":
\n" ); document.write( "It says the sum of the digits is 8:
\n" ); document.write( "x + y = 8
\n" ); document.write( "or
\n" ); document.write( "y = (8-x); use this for substitution
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\n" ); document.write( "\"If 18 is added to the number , the digits of the new numeral are those of the original numeral, but they appear in reversed order.\"
\n" ); document.write( "10x + y + 18 = 10y + x
\n" ); document.write( "10x - x + 18 = 10y - y
\n" ); document.write( "9x + 18 = 9y
\n" ); document.write( "Simplify, divide equation by 9
\n" ); document.write( "x + 2 = y
\n" ); document.write( "Substitute (8-x) for y
\n" ); document.write( "x + 2 = 8 - x
\n" ); document.write( "x + x = 8 - 2
\n" ); document.write( "2x = 6
\n" ); document.write( "x = \"6%2F2\"
\n" ); document.write( "x = 3
\n" ); document.write( "Then y = 5; the original number = 35
\n" ); document.write( ":
\n" ); document.write( "Check solution in the statement;
\n" ); document.write( "\"If 18 is added to the number , the digits of the new numeral are those of the original numeral, but they appear in reversed order.\"
\n" ); document.write( "18 + 35 = 53; confirms our solution
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\n" ); document.write( ":
\n" ); document.write( "The sum of the digits is 8. The number is 16 less than the product of 3 and the number represented when the digits are interchanged.
\n" ); document.write( ":
\n" ); document.write( "Let x = 10's digit of the original number
\n" ); document.write( "Let y = units digit of the original number
\n" ); document.write( "The number = 10x + y
\n" ); document.write( ":
\n" ); document.write( "It says the sum of the digits is 8:
\n" ); document.write( "x + y = 8
\n" ); document.write( "or
\n" ); document.write( "y = (8-x); use this for substitution
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\n" ); document.write( "\"The number is 16 less than the product of 3 and the number represented when the digits are interchange\"
\n" ); document.write( "10x + y = 3(10y+x) - 16
\n" ); document.write( "10x + y = 30y + 3x - 16
\n" ); document.write( "10x - 3x = 30y - y - 16
\n" ); document.write( "7x = 29y - 16
\n" ); document.write( "Substitute (8-x) for y:
\n" ); document.write( "7x = 29(8-x) - 16
\n" ); document.write( "7x = 232 - 29x - 16
\n" ); document.write( "7x + 29x = 232 - 16
\n" ); document.write( "36x = 216
\n" ); document.write( "x = \"216%2F36\"
\n" ); document.write( "x = 6
\n" ); document.write( "then y = 2; the number = 62
\n" ); document.write( ":
\n" ); document.write( "Check solution in the statement:
\n" ); document.write( "\"The number is 16 less than the product of 3 and the number represented when the digits are interchange\"
\n" ); document.write( "62 = 3(26) - 16
\n" ); document.write( "62 = 78 - 16; confirms out solutions
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