SOLUTION: The sum of the digits of a 2-digit number is 15. The digits are reversed when 27 is subtracted from given number. What is the the two-digit number?

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Question 1058733: The sum of the digits of a 2-digit number is 15. The digits
are reversed when 27 is subtracted from given number.
What is the the two-digit number?
Found 3 solutions by Edwin McCravy, ikleyn, Alan3354:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
The sum of the digits of a 2-digit number is 15. The digits
are reversed when 27 is subtracted from given number.
What is the the two-digit number?
The tens digit = t
The units digit = u
The number = 10t+u
The number reversed = 10u+t

The sum of the digits of a 2-digit number is 15.  

t+u = 15


The digits are reversed when 27 is subtracted from given number.

10t+u - 27 = 10u+t

Which simplifies to

9t-9u = 27

or dividing through by 9

t-u = 3

Adding the two equations:

t+u = 15
t-u =  3
--------
 2t = 18
  t =  9

Substituting in

t+u = 15
9+u = 15
  u =  6

The number is "tens digit, units digit" or 96.

Checking the sum of the digits is 9+6=15.

Subtracting 27 from 96 give 96-27 = 69.

That's 96 with the digits reversed.

So the answer is correct.

Edwin
Answer by ikleyn(52772)   (Show Source): You can put this solution on YOUR website!
.
On reversing digits in 2-digit numbers see the lesson
    - Word problems on interchanging digits of numbers
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this textbook under the topic "Miscellaneous word problems".


Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The sum of the digits of a 2-digit number is 15. The digits
are reversed when 27 is subtracted from given number.
What is the the two-digit number?
-----------
Reversing the digits of a 2-digit number changes the value by 9 times the difference between the digits.
---
A change of 27 --> a difference of 27/9 = 3
=================
t + u = 15
t - u = 3
---------------- Add
2t = 18
t = 9
u = 6
---> 96
==================
No need to write a Master's thesis on it.
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