How do you find four consecutive odd integers such that three times the sum of the first and second is 25 less than the fourth?

First, to set up consecutive odd or even integers you have to add 2 to the previous integer.
Let x be the first integer,
(x + 2), (x + 4), and (x + 6)

Now set up the parameters they give:
3(x + x + 2) = x + 6 - 25
Solving:
Combine like terms and distribute on the left, combine like terms on the right.
3(2x + 2) = x - 19
6x + 6 = x - 19
Subtract x from both sides and subtract 6 from both sides.
5x = -25
Divide both sides by 5
x = -5
x + 2 = -5 + 2 = -3
x + 4 = -5 + 4 = -1
x + 6 = -5 + 6 = 1
Check:
3(-5 + -3) ?=? 1 - 25
-24 ?=? -24 CORRECT

The total amount of different books is 16.

Take away 1 from each, representing the same book they all read.

7 - 1 = 6 , 6 - 1 = 5 , 5 - 1 = 4

Add the three together.

6 + 5 + 4 = 15

Add that one book everyone read.

15 + 1 = 16 different books.

Hope I helped you out.