Your backpack contains 2010 chocolate bars, which you are going to divide between your best friend and yourself. you think you are a nice person, so you will give your best friend more than zero chocolate bars. however, you have been craving chocolate recently, and so you must have at least twice as many chocolate bars as your friend after you finish dividing them. what is the difference between the maximum and minimum number of chocolate bars you can have?

The data is:

You have 2010 chocolate bars.

After you divide the chocolate bars, you must have at least twice the amount that your friend has,

If X is the number of chocolate bars that you have and Y is the number of chocolate bars for your friend, we have that:

X + Y = 2010

X > 2*Y

we can solve this equation by assuming the equality in the second equation, in this way we can get:

X + Y = 2010

X = 2*Y

this will give us the minimum value of X.

Now we can replace the second equation into the first one:

2Y + Y = 2010

3Y = 2010

Y = 2010/3 = 670

So your friend gets 670 bars, and you get 2010 - 670 = 1340 bars.

The maximum number of bars that you can get is when you only gave one bar to your friend, so in this case, we have Y = 1, and X = 2010 - 1 = 2009 bars.