Dining out numbers trick: What's the math behind the magic?

[eplovejoy]

There are many numbers tricks like the following. How do they work?

_____


1. Pick the number of times a week that you would like to go out to eat (more than once but less than 10).

2. Multiply this number by 2

3. Add 5

4. Multiply it by 50

5. If you have already had your birthday this year add 1758...

If you haven't, add 1757.

6. Now subtract the four digit year that you were born.

You should have a three digit number


The first digit of this is your original number (how many times
you want to go out to restaurants in a week).


The next two numbers are your age.

2008 is the only year in which this will work.

[amykhar]

What the answer boils down to is 100x + (2008 - the year you were born) OR
100x + (2007 - the year you were born) The one that works depends on if you have had your birthday yet or not.

For example, I chose 2 times. So my answer is 239

The original equation looks like
50(2x + 5) + 1757 -1968 (I haven't had my birthday yet)

This reduces to 100X + 250 + 1757 - 1968

This in turn reduces to 100x + 2007 - 1968

The reason it's 100x is because your original number is in the hundreds place.

[eplovejoy]

Algebra! Now I get it. So the person who created it probably did the math first and then put it into words so it would astonish -- oh, I don't know -- history and literature majors.

Thank you, Amy. I knew I count on you.