Question

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 .

Answer 1

Assume that the number of 2 digits is xy, where x is the tens and y ,the unit
(Mind you, you can write xy = 10x+y (just like 23 = 2.10 +3))

Let's translate from English to Math language:

1) 5(x+y) = 10x+y-13
2) 4(y+x) = 10y+x-21

a) Expanding and simplifying 1)
5x+5y=10x+y-13 → 5x-4y = 13 (a)

b) Expanding and simplifying 2)
4(y+x) =10y+x-21 → 3x-6y = -21 (b)


Finally solving the system of equation with 2 variables x and y:

a) 5x-4y = 13
b) 3x-6y = -21

gives x =9 and y = 8

Then the number is 98