Let's call the original two digit number xy, where x is the tens digit and y is the ones digit. An algebraic representation of this number is 10x + y.
The sum of the two digit number is 8: x+y=8
When the digits are reversed, the number increases by 36: [10y + x] - [10x + y] = 36
Now we have two equations and two unknown parameters, so we have enough information to find those parameters.
Solve for x:
X=8-y
plug in x:
[10y + 8-y] - [10[8-y]+ y] = 36
simplify:
[9y + 8] - [80-9y] = 36
18y - 72 = 36
y = 108/18 = 6
so if y=6, then x=8-y=8-6=2
so our number is 26. 62 is 36 greater than 26, so everything checks out.
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David W. answered • 11/09/17
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So, Sydney, interesting problem!
Let x be the first digit and y be the 2nd.
x + y = 8, right?
Now, in a two-digit number, the first digit is that digit times 10. 25 = 10[2] + 5, for example.
10y + x = 10x + y + 36. Make sense? Using algebra, we turn that into 9y - 9x = 36. We can divide all of that by 9 to get y - x = 4