SOLUTION: In a two digit number, the sum of the digits is 8, the difference between the number and the number with the digits reversed is 54 what is the number?

Question 1181753: In a two digit number, the sum of the digits is 8, the difference between the number and the number with the digits reversed is 54 what is the number?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
t, tens place
u, units or ones place
, the number

and

.
.

OR

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The other tutor shows a solution that is correct except for one thing.

Their solution uses the difference between A and B to be the absolute value of A-B. That is mathematically incorrect.

They show two possible answers -- 71 and 17; only one of the answers is correct.

In everyday usage, the difference between 71 and 17 is 54, and the difference between 17 and 71 is 54. That's because in everyday language, the order doesn't matter.

Mathematically, the difference between 71 and 17 is 54, but the difference between 17 and 71 is -54. That's because when using "difference" in mathematics, the order DOES matter.

So technically there is only one answer. The original number is 71 and the number with the digits reversed is 17.

Otherwise the solution shown by the other tutor is a good algebraic solution.

For a shortcut to solve the problem quickly without formal algebra, use this fact: the difference between a 2-digit number and that number with its digits reversed is equal to 9 times the difference between the 2 digits.

Since the difference between the two 2-digit numbers is 54, the difference between the two digits is 54/9=6.

Then you have the sum of the two digits being 8 and the difference being 6; formal algebra or a bit of quick mental arithmetic shows the two digits to be 7 and 1.

Then, since the difference between the two 2-digit number is positive, the original number is larger; so the original number is 71 and the other number is 17.

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