Answer to Question #119510 in Physics for Hussain Ousman Darboe

Question #119510
A number of two digits is increased by 9. When the digits are reversed, the sum of the digits is 5. Find the number?
1
Expert's answer
2020-06-02T17:53:53-0400

The original condition is:

The sum of the digits of a number lying between 10 and 100 is 5. When the digits are reversed, the number is increased by 9. Find the number.

Assume that the initial number is


10a+b.10a+b.

If the digits are reversed, the number of two digits is increased by 9:


10b+a=10a+b+9,9b9a=9,ba=1.10b+a=10a+b+9,\\ 9b-9a=9,\\ b-a=1.

The sum of the digits is 5:


a+b=5.a+b=5.

Therefore, we have two simple equation that form a system. The solution of the system


ba=1a+b=5b-a=1\\ a+b=5

is


a=2b=3.a=2\\ b=3.

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