SOLUTION: the sum of the digits of a two digit number is 15.if the number formed by reversing the digits is less than the original number by 27.find the original number

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Question 482623: the sum of the digits of a two digit number is 15.if the number formed by reversing the digits is less than the original number by 27.find the original number

Found 2 solutions by cleomenius, MathTherapy:
Answer by cleomenius(959)   (Show Source): You can put this solution on YOUR website!
Maybe there is a better way to do this, but I found the combinations of single digit numbers that would equal 15; they came to 6,9 and 8,7.
the number 96 fits the critera, 86 -27 = 69.
Cleomenius.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Let the tens digit be T, and the units digit U

As sum of digits = 15, then T + U = 15

The value of this number is: 10(T) + U. or 10T + U, and when reversed, we have: 10(U) + T, or 10U + T

Since the # formed by reversing the digits is 27 less than the original number, then we can say that:

10U + T = 10T + U – 27 --------> – 9T + 9U = -27

We now have the following simultaneous equations:
T + U = 15 _____ (i)
– 9T + 9U = - 27 _____ (ii)
9T + 9U = 135 _______ (iii) ----- Multiplying eq (i) by 9
18U = 108 _______ Adding eq (ii) and eq (iii)

U, or the units digit = , or

Substituting 6 for U in eq (i), we get: T + 6 = 15 ----- T, or the tens digit =

Now, since the tens digit is 9, and the units digit is 6, this makes the number:

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Check
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When 96 (original #) is reversed, it becomes 69. 69 is in fact 27 less than 96 (96 - 69 = 27).

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