SOLUTION: The sum of the digits of a two digit number is 7. When the digits are reversed the value of the number increased by 27. Find the number

Algebra.Com
Question 997835: The sum of the digits of a two digit number is 7. When the digits are reversed the value of the number increased by 27. Find the number
Found 2 solutions by fractalier, solver91311:
Answer by fractalier(6550)   (Show Source): You can put this solution on YOUR website!
Call the tens digit x and the ones digit y.
Thus x + y = 7
Originally the value is 10x + y.
Reversed its value is 10y + x. This is 27 more than the original, so
10y + x = 10x + y + 27
or
-9x + 9y = 27
or
-x + y = 3 now add the first equation and get
x + y = 7
2y = 10
y = 5
x = 2
The original number was 25.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Shortcut Method

If you reverse the digits of a two-digit number, the difference between the original two digit number and the new two-digit number is ALWAYS a multiple of 9. And the difference between the two digits is the value of the multiple. Hence, for your problem, where is the original 10s digit and is the original 1s digit:



And, since the original two-digit number must be smaller than the new two-digit number, meaning

.

Long Method

Same definitions of and

Original two digit number:

New two digit number:







And



Either way, solve the 2X2 system for and

John

My calculator said it, I believe it, that settles it

RELATED QUESTIONS

The sum of the digits of a two-digit number is 7. When the digits are reversed, the... (answered by tmwilliamlin168)
the sum of the digits of a two-digit number is 7. when the digits are reversed, the umbe... (answered by josgarithmetic,MathTherapy)
The sum of the digits of a two digit number is seven. When the digits are reversed,... (answered by checkley79)
The sum of the digits of a two digit number is 7. When the digits of the two digit number (answered by Alan3354)
the sum of two digits of a natural number is 7. when the digits are reversed, the number... (answered by Maths68)
The sum of the digits of a two-digit number is 7. When the digits are exchanged, the... (answered by ikleyn)
The sum of the digits of a two digit number is 7. If the digits are reversed, the number... (answered by lwsshak3)
Pls help out: a number of two digits is increased by 9. When the digits are reversed, the (answered by ankor@dixie-net.com)
The sum of the digits of a two-digit number is 7. When the digits reversed the number is... (answered by ikleyn)