Math Trick Disillusionment

Here is a math trick with fairly common structure, after the trick I will proceed to explain the math behind it. So if you don't want to have the trick be demystified don't read after it.


YOUR AGE BY DINER & RESTAURANT MATH 

It takes less than a minute.
Work this out as you read. Be sure you don't read the bottom until you've worked it out! This is not one of those waste of time things; it's fun.


1. First of all, 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 (just to be bold)


3. Add 5


4. Multiply it by 50 


5. If you have already had your birthday this year add 1757 ... If you haven't, add 1756


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

You should have a three digit number.

The first digit of this was your original number (i.e., how many times you want to go out to restaurants in a week) The next two numbers are YOUR AGE! (Oh YES, it is!!!!!)

I am going to use some algebraic notation for this it shouldn't be too hare to follow. Let's say x=the number you picked in step 1, b=your birth year, and r=result of all the steps.

The problem can be written as
50*(2*x+5)+1757-b=r or if you haven't had your birthday yet 50*(2*x+5)+1756-b=r

it turns out that by simplifying the equations above we get

100x +2007-b=r and 100x+2006-b=r

Looking at the first equation we see the 2007-b this is in fact your age or if you have not had a birthday we subtract 2006.
So we have your age and assuming it is less than 100 we simply add on 100 times your original choice so it ends up in front of your age in the finally calculation.

Interesting to note this trick only works for this year next year the 1757 and 1756 will both need to increase by one. I hope someone else found this at least remotely interesting.

Have a good one