SOLUTION: The sum of the digits of a two-digit number is 5. If 9 is subtracted from the number, the digits will be interchanged. Find the number. I had completed this much: assume ab

Question 1207727: The sum of the digits of a two-digit number is 5. If 9 is subtracted from the number, the digits will be interchanged. Find the number.
I had completed this much:
assume ab is a number, a being in the 10's place and b being in the units place.
ab=10a+b
a+b=5
9-(10a+b)=(10b+a)
But I am now confused on to what to substitute and how to do it.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.

The equation in your post is INCORRECT. The correct equation is (10a+b) - 9 = 10b + a (literal translation from English to Math). It gives 10a - a - 9 = 10b - b 9a - 9 = 9b From a+b = 5, express a = 5-b and substitute it into the last equation 9(5-b) - 9 = 9b 45 - 9b - 9 = 9b 45 - 9 = 9b + 9b 36 = 18b b = 36/18 = 2. So, b= 2; a = 5-b = 5-2 = 3. ANSWER. The number is 10*3+2 = 32.

Solved.

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To see many other similar solved problems on reversing digits, look into the lesson
    - Word problems on reversing digits of numbers
in this site.

Learn the subject from there.

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

Here is an important note regarding the work you show in trying to set up the problem.

The statement of the problem says "if 9 is subtracted from the number..."

You need to pay attention to what the whole phrase says, and not just write math symbols representing the given words.

"9" is SUBTRACTED FROM the number. The mathematical expression representing those words has to show that the 9 is being subtracted:
(the number) minus (9) --> (10a+b)-9 -- not "9-(10a+b)", as you show in your work.

Then a formal algebraic solution can be obtained from this correct expression as shown in the response from the other tutor.

This is a common type of problem on competitive math contest exams. If a formal algebraic solution is not needed, note that when the digits of a 2-digit number are reversed, the difference between the original number and the new number is always 9 times the difference between the two digits.

In this problem, the sum of the two digits is 5, and the difference between the two numbers is 9 = 9*1, so the difference between the two digits is 1.

So the sum of the two digits is 5 and the difference between the two digits is 1; that means the two digits are 2 and 3.

Finally, since 9 was subtracted from the original number to get the new number, the original number is larger than the new number; that makes the original number 32 and the new number 23.

ANSWER: 32

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