Well, my friend, addition is the process by which two numbers are combined to produce a new number, called a "sum." Addition is usually modeled using things placed in baskets. A common textbook example works thusly,
- You have a basket with five apples.
- Ted has a basket with three apples.
- If Ted puts all of his apples in your basket, how many apples do you now have?
This example is misleading, however, because it implies that you are, right now, not tied up in Ted's basement. I told you to never talk to him. He's too cunning for children like you to withstand his advances. But you went and talked to him anyway, and now you're scared, and want me to come to the rescue; well that is a damn shame my friend. I wish I could help, but I'm a little hungry as is. What's the point in helping you if I can't even help myself, eh? Maybe when you're a little older you will be able to realize these things.
What's that? You're crying now!? Oh, and Ted's bringing more apples for your basket? Well, in that case,
- The number of apples in your basket is currently equal to 8.
- The number of apples in Ted's basket was equal to 0.
- Ted went back to the apple orchard that he frequents (usually looking for more children), and picks another 15 apples.
- Ted comes back to the basement and takes 4 of your apples, gives you 9 of his, then takes another 3 of your old ones.
- From my former knowledge, I know that Ted has a serious apple-trading fetish.
By simply adding number 4 and number 5 together, I now know that you are in some serious trouble.
Fine. I'll come get you.
You're such a wuss, you know that?! Well, I should be able to ride my bike over there in about 15 minutes. Think you can hold him off for that long? Haha, I'm just kidding. It doesn't take that long for the apple-fetish to kick in. I'll probably stop him about halfway through. But, while you wait for me, I'll give you this simple addition equation to solve.
- Let's say we have 15 minutes until I come get you from Ted's basement, and luckily for you, he's gone back to the orchard to get a few more apples.
- The orchard is about 3 minutes from his house.
- It will take him 2 minutes to pick the apples he wants, followed by another 3 minute trip back to his house.
- It will then take him 4 minutes to finish trading apples with you again.
Given this information, how many minutes will you have to stall Ted before I get there, or risk losing a lot more than just a few apples?
Good luck with that.
OK, I'm here.
OK, so I come to help you out, but you trick me, attack me, and trade me to Ted for your own freedom. I have to say, that was kind of a douche move. I don't like your methods, but I have to respect your problem-solving abilities. Maybe the addition I've been teaching you has paid off. Well, regardless, I'll see you at home. You're dead, but enjoy yourself until I get back. What's that? You have an equation for me?
- I have zero apples, and Ted has 13 apples.
- Ted refuses to use the apples that he traded with you to trade with me, and it will take him 12 minutes to get back with the more apples to trade.
- If he gets 20 apples, 8 for me, and 12 for himself, how many apples will he have to give me for the two of us to have an equal amount of apples?
Well...I don't know. I'm really not very good at math, you know. But, I can't figure out how the 12 minutes he'll be gone has anything to do with the equation?
Oh, that's how long I have to get out of these ropes while I think about the answer... I see...