three bookshelves contain a total of 35 books. The first and second shelves contain a total of 20 books. the second and third shelves contain a total of 28 books. how many books are on the second shelf then?

first one --x

2nd one -- y
3rd one -- 35-x-y

x+y = 20
y + (35-x-y) = 28 --- > x = 7

(then 7+y =20 ---> y = 13
35-x-y = 35-7-13 = 15

first shelf has 7
2nd shelf has 13
third has 15

check:
1st plus 2nd = 7+13 = 20 , check!
2nd plus 3rd = 13+15 = 28, check!
all is good

Let's solve this step-by-step.

Step 1: Determine the number of books on the first and second shelves.
Let's assume the number of books on the first shelf is x.
The number of books on the second shelf would then be (20 - x), as the total number of books on the first and second shelves is 20.

Step 2: Determine the number of books on the second and third shelves.
Again, let's assume the number of books on the second shelf is y.
The number of books on the third shelf would then be (28 - y), as the total number of books on the second and third shelves is 28.

Step 3: Write equations based on the given information.
From the information provided, we have:
x + (20 - x) = 20 (Equation 1)
y + (28 - y) = 28 (Equation 2)

Step 4: Solve the equations.
Simplifying Equation 1, we get:
20 = 2x
x = 10

Substituting the value of x into Equation 2, we get:
y + (28 - y) = 28
y - y = 0
Therefore, y can be any value.

Step 5: Calculate the number of books on the second shelf.
Since y can be any value, we cannot determine the exact number of books on the second shelf.

To solve this problem, let's break it down step by step.

We are given three bookshelves, and their total number of books. Let's denote the number of books on the first shelf as A, the second shelf as B, and the third shelf as C.

According to the given information:

1. The first and second shelves contain a total of 20 books. This can be expressed as: A + B = 20.

2. The second and third shelves contain a total of 28 books. This can be expressed as: B + C = 28.

We can solve these two equations simultaneously to find the values of A, B, and C.

First, let's subtract equation 1 from equation 2 to eliminate variable B:

(B + C) - (A + B) = 28 - 20
C - A = 8

Now, we have another equation: C - A = 8.

Since we don't know the exact values of A, B, and C, we cannot directly solve for any of them. However, we can use this equation to determine the relationship between C and A.

Let's analyze the possible values:

1. If C is greater than A by 8, it means C = A + 8.
2. If A is greater than C by 8, it means A = C + 8.

Since the problem does not provide any additional information, we cannot determine the specific values for A, B, and C. However, we can still find the value for B.

Let's go back to the equation A + B = 20. By substituting C = A + 8 into this equation, we get:

A + B = 20
A + (C + 8) = 20
A + C + 8 = 20
(A + C) + 8 = 20
28 + 8 = 20
B + 8 = 20
B = 12

Therefore, there are 12 books on the second shelf.