Answer:
78
Step-by-step explanation:
Interchanging the digits of a 2-digit number changes the value by a multiple of 9. The multiple is the difference between the digits of the number.
So, we have two digits that add to 15, and have a difference of 9/9 = 1. Since you're familiar with your addition facts, you know that the two digits are 7 and 8. Since the number we're looking for is the smallest of the numbers you can make with those digits, ...
the original number is 78.
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More formally, let t and o represent the tens and ones digits of the original number.
t + o = 15 . . . . . . the sum of digits is 15
(10o +t) - (10t +o) = 9 . . . . swapping digits increases the value by 9
The latter equation simplifies to ...
9o -9t = 9 . . . . collect terms
o - t = 1 . . . . . . divide by 9 . . . (note the difference of digits is 9/9=1)
Adding this to the first equation gives ...
(t +o) +(o -t) = (15) +(1)
2o = 16
o = 8
t = o -1 = 7
The tens digit is 7 and the ones digit is 8: 78.
