SOLUTION: The sum of the digits of a two-digit number is 13. If the digits are reversed, the new number is 4 less than twice the original number. Find the original number. I an very confu

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Question 133852: The sum of the digits of a two-digit number is 13. If the digits are reversed, the new number is 4 less than twice the original number. Find the original number.
I an very confused with this problem.
It's be greatly appreciated if I could get help!
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
10s digit: x
1s digit: y

The original number: , because a number like 24 could be represented as

Reversing the digits makes a new number:

Twice the original number is and 4 less than that is which we know to be equal to the new number, so:



Simplify:





Since we know that the sum of the digits is 13, we can say , or in other words,

Substitute:





So the 10s digit of the original number (and the ones digit of the new number) is 4. Therefore the ones digit of the original number must be , and the original number must be 49.

Check:
Number is: 49

which is the original number with the digits reversed.
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