Edward C. answered • 04/13/15

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Caltech Grad for math tutoring: Algebra through Calculus

This one's actually pretty easy to solve by estimation since there aren't that many two digit numbers with the sum of the digits being equal to 4. But I'll show you how to do problems like this in general.

If the tens digit of the number is X and the ones digit is Y then the number is equal to 10*X + Y

If you reverse the digits then the number is equal to 10*Y + X

If reversing the digits decreases the number by 36 then

10*Y + X = 10*X + Y - 36

The sum of the digits is 4 so X + Y = 4 ==> X = 4 - Y

Substitute this value of X into the 1st equation

10*Y + (4 - Y) = 10*(4 - Y) + Y - 36

9*Y + 4 = 40 - 9*Y - 36

18*Y = 0

Y = 0

So X = 4 - 0 = 4 and the number is 40

Check: 40 - 04 = 36