Question 1181753
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The other tutor shows a solution that is correct except for one thing.<br>
Their solution uses the difference between A and B to be the absolute value of A-B.  That is mathematically incorrect.<br>
They show two possible answers -- 71 and 17; only one of the answers is correct.<br>
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.<br>
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.<br>
So technically there is only one answer.  The original number is 71 and the number with the digits reversed is 17.<br>
Otherwise the solution shown by the other tutor is a good algebraic solution.<br>
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.<br>
Since the difference between the two 2-digit numbers is 54, the difference between the two digits is 54/9=6.<br>
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.<br>
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.<br>