document.write( "Question 990801: the tens' digit of a number is 3 less than the units' digits. 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 #610894 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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let a = the 10's digit
\n" ); document.write( "let b = the units
\n" ); document.write( "then
\n" ); document.write( "10a + b = the number
\n" ); document.write( ":
\n" ); document.write( "write an equation for each statement
\n" ); document.write( ":
\n" ); document.write( " the tens' digit of a number is 3 less than the units' digits.
\n" ); document.write( "a = b - 3
\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( " $\"%28%2810a%2Bb-3%29%29%2F%28%28a%2Bb%29%29\"$ = 4
\n" ); document.write( "10a + b - 3 = 4(a+b)
\n" ); document.write( "10a + b - 3 = 4a + 4b
\n" ); document.write( "10a - 4a = 4b - b + 3
\n" ); document.write( "6a = 3b + 3
\n" ); document.write( "simplify, divide by 3
\n" ); document.write( "2a = b + 1
\n" ); document.write( "Replace a with (b-3) from the first statement
\n" ); document.write( "2(b-3) = b + 1
\n" ); document.write( "2b - 6 = b + 1
\n" ); document.write( "2b - b = 1 + 6
\n" ); document.write( "b = 7
\n" ); document.write( "then
\n" ); document.write( "a = 7 - 3
\n" ); document.write( "a = 4
\n" ); document.write( ":
\n" ); document.write( " what is the original number? 47
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "See if that checks out in the 2nd statement
\n" ); document.write( " $\"%2847+-+3%29%2F%284+%2B+7%29\"$ =
\n" ); document.write( " $\"44%2F11\"$ = 4
\n" ); document.write( " \n" ); document.write( "

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