HOW DOES “CHOCOLATE MATH&lrdquo; WORK?

So, how does that Chocolate Math thing work?

How is it that we do these seemingly random arithmetic operations, and always end up with such a
predictable answer:

a three-digit
number, where the first digit is the number we started with, and the last two digits are our age?

It's a beautiful example of: NUMBERS HAVE LOTS OF DIFFERENT NAMES!

Here are the details, for those of you with inquiring minds:

Let
[beautiful math coming... please be patient]
$\,x\,$ be the number of times that you like to eat chocolate each week
$\,(1 \le x \le 9)\,$.

Write your age as
[beautiful math coming... please be patient]
$\,10T + W\,$.

For example, if you're $\,46\,$, then
[beautiful math coming... please be patient]
$\,46 = 10\cdot 4 + 6\,$, so $\,T = 4\,$ and $\,W = 6\,$.

Okay, now let's go through each of the steps of “Chocolate Math” with an algebraic expression depending on $\,x\,$, $\,T\,$, and $\,W\,$:

How many times a week do you like to eat chocolate? | [beautiful math coming... please be patient] $x$ |

Multiply by $\,2\,$. | $2x$ |

Add $\,5\,$. | $2x+5$ |

Multiply by $\,50\,$. | [beautiful math coming... please be patient] $50(2x + 5)$ |

Subtract the year you were born. |
Already had birthday: Haven't yet had birthday: |

Now, let's look at each of the resulting expressions:

Already had birthday:

Haven't yet had birthday:

In both cases, we get the expression $\,100x + 10T + W\,$,

which is the digit $\,x\,$ in the hundreds place,

the digit $\,T\,$ in the tens place,

and the digit $\,W\,$ in the ones place!

VOILA!!