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.