Question

The sum of a two-digit number and the number formed by reversing the digits 88. If the difference of the digits is 2, determine the number.

Answer 1

Let x = the 10's digit
Let y = the units
:
Write an equation for each statement:
:
"the sum of a two digit number and the number formed by reversing the order digits is 88."
(10x + y) + (10y + x) = 88
11x + 11y = 88
Simplify, divide by 11
x + y = 8
:
"if difference of the digits is 2 and the units digit is greater."

y - x = 2
we can use elimination with the 1st equation
y - x = 2
y + x = 8
--------------Adding eliminates x, find y
2y = 10
y = 5 is the units digit
then
5 - 2 = 3 is 10's digit
:
35 is the number
:
:
:
Check solution in the 1st statement:
the sum of a two digit number and the number formed by reversing the order digits is 88.
35 + 83 = 88

Answer 2

let the digits of the number be x,y
then xy +yx = 88
x- y = 2
Take the set 2 of numbers whose difference is 2
They can be 1,3 or 2,4 or 3,5 or 4,6.......................
verify the condition for the possible sets
let us start with 4,6
46 + 64 =110 which exceeds 88
so next verification would be for 3,5
35 + 53 = 88
SO the set is 3,5 and the number nay be either 35 or 53