document.write( "Question 198445: The units digit of a 2-digit number exceeds the tens digit by 3. If the number, increased by 2, is divided by the sum of the digits decreased by 3, the quotient is 6. Find the number. \n" ); document.write( "

Algebra.Com's Answer #148954 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The units digit of a 2-digit number exceeds the tens digit by 3.
\n" ); document.write( " If the number, increased by 2, is divided by the sum of the digits decreased
\n" ); document.write( " by 3, the quotient is 6. Find the number.
\n" ); document.write( ":
\n" ); document.write( "two digits: x, y; the number: 10x + y
\n" ); document.write( ":
\n" ); document.write( "write an equation for each statement:
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\n" ); document.write( "\"The units digit of a 2-digit number exceeds the tens digit by 3.\"
\n" ); document.write( "y = x + 3
\n" ); document.write( ":
\n" ); document.write( "\" If the number, increased by 2, is divided by the sum of the digits decreased
\n" ); document.write( " by 3, the quotient is 6.\"
\n" ); document.write( " $\"%28%2810x+%2B+y+%2B+2%29%29%2F%28%28x+%2B+y+-+3%29%29\"$ = 6
\n" ); document.write( "Replace y with (x+3)
\n" ); document.write( " $\"%28%2810x+%2B+%28x%2B3%29+%2B+2%29%29%2F%28%28x+%2B+%28x%2B3%29+-+3%29%29\"$ = 6
\n" ); document.write( "Do the math
\n" ); document.write( " $\"%28%2811x+%2B+5%29%29%2F%28%282x%29%29\"$ = 6
\n" ); document.write( ":
\n" ); document.write( "Multiply both sides by 2x
\n" ); document.write( "11x + 5 = 2x(6)
\n" ); document.write( "5 = 12x - 11x
\n" ); document.write( "x = 5
\n" ); document.write( "and
\n" ); document.write( "y = 5 + 3
\n" ); document.write( "y = 8
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\n" ); document.write( "The number: 58
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\n" ); document.write( "Check solution in the statement:
\n" ); document.write( "\"If the number, increased by 2, is divided by the sum of the digits decreased
\n" ); document.write( " by 3, the quotient is 6.\"
\n" ); document.write( " $\"%28%2858+%2B+2%29%29%2F%28%285+%2B+8+-+3%29%29\"$ = 6\r
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