A businessman rode a camel to a 1,000-kilometer desert to sell 3,000 carrots. The camel could only carry 1,000 carrots at a time. The camel had to eat one carrot per day. How many carrots could the businessman sell in the end?

tips1

Assume the starting point is A and the end point is D
In order to fully transport the 3000 sticks, it takes three walks
The third time to reach the end point D a>
The first and second time we stopped halfway and put down some radishes
So we assume that the 1,000-kilometer road is divided into 3 sections:
First The length of the segment is x, the length of the second segment is y, and the length of the third segment is z
Specifically, assume AB = x, BC = y, CD = z

tips2

x walked 5 times, y walked 3 times, z walked 1 time

tips3

The maximum number of radishes we hope to carry when walking z is 1,000 radishes
means: there are 1,000 radishes left when we arrive at C for the last time
The first equation comes out 3000 - 5x - 3y = 1000

tips4

We hope to put down the most radishes at C
This means that when we return from C to B on the second return trip, the number of radishes should be exactly 0

tips5

We hope that no extra radish will leak out at point B
So how do you express the radish at point B
First, go back and forth for the first time, put down point B 1000-2x radishes
Then, when passing by B for the second time, the 1000-x radishes on hand need to be replenished, so B is left with 1000-3x radishes
Then on the second return trip, according to tips 4, pass B and get x radishes, B is left with 1000-4x radishes
Pass B for the last time, and add 1000 more radishes. At this time, B is left with 1000 -5xradish

tips6

1000-5x = 0 -》 a> So after taking the last 1000 and the radish and walking the length of z, there are still 533.3 radishes