SOLUTION: the sum of the digits of a two-digit number is 10. If the digits are reversed, the number is increased by 72. What is the original number?

Question 174725: the sum of the digits of a two-digit number is 10. If the digits are reversed, the number is increased by 72. What is the original number?
Found 2 solutions by Mathtut, josmiceli:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
let the two digits be a and b
:
a+b=10..........eq 1
:
10b+a=10a+b+72--->9a-9b=-72..eq 2
:
re write eq 1 to a=10-b and plug it into eq 2
:
9(10-b)-9b=-72
:
90-9b-9b=-72
:
-18b=-162
:

:
original number

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Call the units digit
Call the tens digit
Given:

The actual value of the number is

The value of the number with the digits reversed is

Given:

(1)
(2)
Multiply both sides of (2) by and add to (1)
(1)
(2)
(3)

The original number is 19
check:

OK
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