Missing Middle Digits

Today's question isn't long and isn't hard, but it makes you think a little. Tomorrow I'll have a nicer question, with an ellipse. Until then, you'll have to work your mind on digits.

In a two digit number, the units digit is bigger than the tens digit by 4. First, you add 1 between the two digits and call it x. Then, you add 5 to the right of the units digit of the original number and call it y. x + y = 692. What is the two digit number?

Let's take this step by step:
First, the original number is _ _.

x is _ 1 _
y is _ _ 5
x + y is 692

Now we can find the values of the units digit, since we know that the units digit + 5 gives 12 (it can't give 2, obviously). This makes the units digit 7.

x is _ 1 7
y is _ 7 5

As you can see, adding the two numbers will leave the hundreds digits untouched. As a result, the two hundreds digits, which are equal, must add up to 6. This makes the hundreds digit 3.

The two numbers are 317 and 375, and the original number is 37.

Short, nice, easy. Tomorrow will be a little harder, I promise.
Nadav

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