Peter had 144 books and donated them to four schools. When Peter checked the number of books given to each school, he found out that the difference of the number of books between School A and School B was 4; between School B and School C was 3; between School C and School D was 2. School A had the most number of books, but received less than 40 books. How many books did School D get?
Answer
Denote the number of books received by the four schools a, b, c and d, respectively.
Since a is the largest, b must equal a-4.
c differs 3 from b, and can be either a-1 or a-7.
If c=a-1, then d must be a-3, which implies a+(a-4)+(a-1)+(a-3)=144, a=38, and a-3=35.
If c=a-7, then d can be either a-5 or a-9. However, it can be checked that in either case, a>=40.
Therefore, School D got 35 books.
