SOLUTION: The difference between the digits of a two digits number is 1. The number itself is 1 more than 5 times the sum?

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Question 703199: The difference between the digits of a two digits number is 1. The number itself is 1 more than 5 times the sum?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the number takes the expanded form, x*10+y*1, and the digits are x and y.

(1) Either x-y=1, OR y-x=1.
(2) The other description translates to 10x+y=1+5(x+y)

Using equation #2, 10x+y=1+5x+5y,
5x+y=1+5y
5x-4y=1

If we now chose from eq.#1, y-x=1, we find x=y-1. Substitute this into 5x-4y=1.
5(y-1)-4y=1
couple more steps,
y=6
Therefore x=5

Answer: 56