Three student teams collected 65 books for the school library. The first team collected 10 fewer books than the second team and the third team collected 30% of the number of books collected by first and second teams together. How many books did each team collect?

There are three teams that collected a total of 65 books

Team 1 - x

Team 2 - x + 10

As team 2 collected 10 books more than team 1

Team 3 - 30% of (x + x + 10)

Team 3 collected 30% of the books that team 1 and team 2 collected in total

The equation for the total number of books is;

x + x + 10 + 0.3 (2x+10) = 65

2x + 10 + 0.6x + 3 = 65

2.6x + 13 = 65

2.6x = 52

x = 20

Team 1-20 books

Team 2 - 30 books and

Team 3 - 15 books

Given:

3 student teams

65 total number of books collected

first team collected 10 fewer books than the second team

the third team collected 30% of the number of books collected by first and second teams together

Let x represent the books collected by the 2nd team.

1st team: (x - 10)

2nd team: x

3rd team: 30%[x + (x-10) ]

(x-10) + x + 30%[x + (x - 10) ] = 65

x - 10 + x + 0.3x + 0.3x - 3 = 65

x + x + 0.3x + 0.3x = 65 + 10 + 3

2.6x = 78

x = 78/2.6

x = 30

1st team: x - 10 → 30 - 10 = 20

2nd team: x → 30

3rd team: 30%[x + (x-10) ] → 0.3 (30 + 30 - 10) = 0.30 (50) = 15

20 + 30 + 15 = 65

1st team got 20 books.

2nd team got 30 books.

3rd team got 15 books.

For a total of 65 books.