Prep 的一个数学题

westminster

A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

• 
  10,700
  
• 
  10,800
  
• 
  10,900
  
• 
  11,000
  
• 
  11,100
  
  

请问这个题怎么解呢？谢谢！

westminster

答案是 11,000

lijj0410

设那个最小的population为a，那么其他10个districts里面最大的population不超过1.1a（来自a+10%a=110%a），即全部的11个population都在a到1.1a之间，因为总和是132000是确定的，那如果想求一个district最小，那就让其他10个districts尽可能的大，即10个都是1.1a
11个population相加a+10*1.1a>=总数132000
12a>=132000
a>=11000

westminster

lijj0410 发表于 2018-9-11 23:24
设那个最小的population为a，那么其他10个districts里面最大的population不超过1.1a（来自a+10%a=110%a）， ...

太棒了！感谢！