Three students Annie, Betty and Chris had some books that their Mathematics teacher gave. Annie got 1/3 of the number of books that Betty and Chris received. Betty got 1/5 of the number of books which Annie and Chris received. If Chris received 5 books more than Betty, how many books in total did the teacher gave the three students?
at the start:
Annie --- a
Betty --- b
Chris ---- c
a = (1/3)(b+c)
3a - b - c = 0 *
b = (1/5)(a+c)
5b - a - c = 0 **
subtract ** from *
4a -6b = 0
a = 3b/2 ***
more info:
c = b+5
sub into **
5b - 3b/2 - (b+5) = 0
times 2
10b - 3b - 2b = 10
5b = 10
b = 2 , then c = 7, and a = 3
put it all together in a proper conclusion.