Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
five times the sum of the digits of a two-digit number is 13 less than the original number. if you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number.
(hint: you can use variables to represent the digits of a number. if a two-digit number has the digit x in tens place and y in one’s place, the number will be 10x + y. reversing the order of the digits will change their place value and the reversed number will 10y + x.)
the difference of the original two-digit number and the number with reversed digits is
.

Let the tens digit of the original number be represented by x.  Let the ones digit be y.

The original number is then 10x + y, and the reversed number is 10y + x.

"Five times the sum of the digits is 13 less than the original number" becomes:



"Four times the sum of its digits is 21 less than the reversed number" becomes:



Work with the first equation until it is simpler:



Do the same thing with the second equation:



Now you have a system of two equations to solve.



To eliminate x, multiply the first equation by 3 and multiply the second equation by 5



Add the two equations.



Aha!  The one digit of the original number is 8.  To find y, put x = 8 into any equation containing both x and y.



Sweet!  The tens digit of the original number is 9.  The original number is 98 and the reversed number is 89.

Their difference is 9.

Most of the people don’t make the sense of taking it