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
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.
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
