document.write( "Question 1055937: A two igit number is 3 more than 4 time the sum of its digits. If 18 is adfef to the number, the digits are reversed. Find the number.solve by using two variable.of 9class \n" ); document.write( "

Algebra.Com's Answer #671094 by ikleyn(52805) $\"\"$ $\"About$

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\n" ); document.write( "A two digit number is 3 more than 4 time the sum of its digits. If 18 is $\"highlight%28cross%28adfef%29%29\"$ added to the number, the digits are reversed.
\n" ); document.write( "Find the number. Solve by using two variable. of 9 class
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document.write( "Let \"a\" be the tens digit of the number and \"b\" be its ones digit.\r\n" );
document.write( "So the number itself is 10a + b.\r\n" );
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document.write( "You are given\r\n" );
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document.write( "10a + b = 4(a+b) + 3       (1)    (\"A two digit number is 3 more than 4 time the sum of its digits\")\r\n" );
document.write( "(10a + b) + 18 = 10b + a   (2)    (\"If 18 is added to the number, the digits are reversed.   Notice:  10b + a  is  10a + b after reversing digits !)\r\n" );
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document.write( "So, you have this system of two equations (1) and (2) for the two unknowns \"a\" and \"b\".\r\n" );
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document.write( "Let us rewrite the system in the standard form:\r\n" );
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document.write( "6a - 3b =   3,     (1')\r\n" );
document.write( "9a - 9b = -18.     (2')\r\n" );
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document.write( "Cancel common factor 3 in (1') (in both sides)  and  9  in (2') (both sides). You will get\r\n" );
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document.write( "2a - b =  1,       (1'')\r\n" );
document.write( " a - b = -2.       (2'')\r\n" );
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document.write( "Now distract equation (2'') from equation (1''). You will get\r\n" );
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document.write( "a = 3.\r\n" );
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document.write( "Then from (2'')  b = a+2 = 3+2 = 5.\r\n" );
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document.write( "Answer.  Your number is 35.\r\n" );
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document.write( "Check.   Check it on your own.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to see more solved problems on reversing digits in numbers, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Word problems on interchanging digits of numbers\r
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