document.write( "Question 402585: When a certain two digit number is divided by the number obtained by reversing the digits, the quotient is 2 and the remainder is 7. If the number is divided by the sum of its digits, the quotient is 7 and the remainder is 6. Find the number \n" ); document.write( "
Algebra.Com's Answer #284747 by ankor@dixie-net.com(22740)\"\" \"About 
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When a certain two digit number is divided by the number obtained by reversing
\n" ); document.write( " the digits, the quotient is 2 and the remainder is 7.
\n" ); document.write( " If the number is divided by the sum of its digits, the quotient is 7 and the remainder is 6.
\n" ); document.write( "Find the number
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\n" ); document.write( "The two digit number: x = the 10's digit; y = the units
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\n" ); document.write( "\"When a certain two digit number is divided by the number obtained by reversing
\n" ); document.write( " the digits, the quotient is 2 and the remainder is 7.\"
\n" ); document.write( "\"%28%2810x%2By-7%29%29%2F%28%2810y%2Bx%29%29\" = 2
\n" ); document.write( "10x + y - 7 = 2(10y + x)
\n" ); document.write( "10x + y - 7 = 20y + 2x
\n" ); document.write( "10x - 2x = 20y - y + 7
\n" ); document.write( "8x = 19y + 7
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\n" ); document.write( "\"If the number is divided by the sum of its digits, the quotient is 7 and the remainder is 6.\"
\n" ); document.write( "\"%28%2810x%2By-6%29%29%2F%28x%2By%29\" = 7
\n" ); document.write( "10x + y - 6 = 7(x+y)
\n" ); document.write( "10x + y - 6 = 7x + 7y
\n" ); document.write( "10x - 7x = 7y - y + 6
\n" ); document.write( "3x = 6y + 6
\n" ); document.write( "divide by 3
\n" ); document.write( "x = (2y + 2)
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\n" ); document.write( "Substitute (2y+2) for x in the 1st simplified equation
\n" ); document.write( "8(2y + 2) = 19y + 7
\n" ); document.write( "16y + 16 = 19y + 7
\n" ); document.write( "16 - 7 = 19y - 16y
\n" ); document.write( "9 = 3y
\n" ); document.write( "y = 3
\n" ); document.write( ":
\n" ); document.write( "Find x
\n" ); document.write( "x = 2y + 2
\n" ); document.write( "x = 3(3) + 2
\n" ); document.write( "x = 8
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\n" ); document.write( "83 is the original number
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\n" ); document.write( "Check solution in the statement:
\n" ); document.write( "When a certain two digit number is divided by the number obtained by reversing
\n" ); document.write( " the digits, the quotient is 2 and the remainder is 7.\"
\n" ); document.write( "\"83%2F38\" = 2 with remainder of 7
\n" ); document.write( ":
\n" ); document.write( "do the same with the statement:
\n" ); document.write( "\" If the number is divided by the sum of its digits, the quotient is 7 and the remainder is 6.\"
\n" ); document.write( "\"83%2F11\" = 7 with a remainder of 6 \n" ); document.write( "
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