document.write( "Question 475433: The tens digit of a number is 3 less than the units digit. If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3. What is the original number? \n" ); document.write( "

Algebra.Com's Answer #326115 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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x = the 10's digit
\n" ); document.write( "y = the units
\n" ); document.write( "10x + y = the number
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\n" ); document.write( "\"The tens digit of a number is 3 less than the units digit.\"
\n" ); document.write( "y - x = 3
\n" ); document.write( "y = (x+3)
\n" ); document.write( ":
\n" ); document.write( "If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3.
\n" ); document.write( " $\"%2810x%2By-3%29%2F%28x%2By%29\"$ = 4
\n" ); document.write( "multiply both sides by (x+y)
\n" ); document.write( "10x + y - 3 = 4(x+y)
\n" ); document.write( "10x + y - 3 = 4x + 4y
\n" ); document.write( "10x - 4x = 4y - y + 3
\n" ); document.write( "6x = 3y + 3
\n" ); document.write( "Simplify divide by 3
\n" ); document.write( "2x = y + 1
\n" ); document.write( "replace y with (x+3)
\n" ); document.write( "2x = x + 3 + 1
\n" ); document.write( "2x - x = 4
\n" ); document.write( "x = 4 is the tens digit
\n" ); document.write( "then
\n" ); document.write( "y = 4 + 3
\n" ); document.write( "y = 7 is the units
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\n" ); document.write( "47 is the original number
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\n" ); document.write( "See if that works in the statement:
\n" ); document.write( "\"If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3.\"
\n" ); document.write( " $\"47%2F11\"$ = 4 a remainder of 3\r
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