Let's say district y is the small district. We want to figure out how to make it as small as possible. Since the biggest district can't be more than 10% bigger, we want to (1) minimize the size of the biggest district, (2) try to make the smallest district be the biggest district divided by 110%, to make it as small as possible.
We minimize the size of the biggest district by making all 10 districts that aren't the smallest district be the exact same size. You can see that if you reduced the size of one of these, you would have to increase the size of another one to keep the population the same.
So, the total population is expressed as:
10x + y = 132,000 (where x is the size of the other districts)
Since we want to minimize y,we also have:
x = 1.1y
Now we plug in:
10(1.1y) + y = 132,000
12y = 132,000
y = 11,000
Make sense?
Best wishes,
Tatiana
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