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Let's break down the problem in the image step by step and solve it systematically.

### Given information:
1. The total number of books by Anwar (A), Bertha (B), and Cassey (C) is 100:
   \[
   A + B + C = 100
   \]

2. The total number of books by Anwar and Bertha is 60:
   \[
   A + B = 60
   \]

3. The total number of books by Anwar and Cassey is 70:
   \[
   A + C = 70
   \]

4. We are asked to find the sum of two times the number of books by Anwar, three times the number of books by Bertha, and the number of books by Cassey:
   \[
   2A + 3B + C
   \]

### Step 1: Solve for the individual values of A, B, and C

From the second equation:
\[
A + B = 60
\]
We can express \(B\) as:
\[
B = 60 - A
\]

From the third equation:
\[
A + C = 70
\]
We can express \(C\) as:
\[
C = 70 - A
\]

### Step 2: Substitute these into the first equation

Substitute the expressions for \(B\) and \(C\) into the first equation:
\[
A + (60 - A) + (70 - A) = 100
\]

Simplify:
\[
A + 60 - A + 70 - A = 100
\]
\[
130 - A = 100
\]

Solve for \(A\):
\[
A = 30
\]

### Step 3: Solve for \(B\) and \(C\)

Using \(A = 30\) in the equations for \(B\) and \(C\):

\[
B = 60 - A = 60 - 30 = 30
\]
\[
C = 70 - A = 70 - 30 = 40
\]

So, \(A = 30\), \(B = 30\), and \(C = 40\).

### Step 4: Calculate \(2A + 3B + C\)

Now, we can calculate the required expression:
\[
2A + 3B + C = 2(30) + 3(30) + 40
\]
\[
= 60 + 90 + 40
\]
\[
= 190
\]

### Final Answer:
The sum of two times the number of books by Anwar, three times the number of books by Bertha, and the number of books by Cassey is **190**.

---

Do you need further clarification on any step? 

Here are 5 related questions to deepen understanding:
1. How would the solution change if the total number of books were different?
2. Can you create another similar problem with different numbers?
3. What if we had four people with different book totals instead of three?
4. How could this system of equations be solved graphically?
5. Can you express the solution in terms of matrices?

**Tip:** When solving systems of linear equations, always check if you can simplify one equation by substitution, as this often makes the process faster.

Total banyak buku Anwar, Bertha, dan Cassey adalah 100 buku. Total banyak buku Anwar dan Bertha adalah 60 buku. Total banyaknya buku Anwar dan Cassey adalah 70 buku. Hasil penjumlahan dari dua kali banyak buku Anwar, tiga kali banyak buku Bertha, dan banyak buku Cassey adalah ....

Learn how to solve a system of linear equations involving the total number of books owned by Anwar, Bertha, and Cassey. Using key algebraic techniques, find the sum of two times Anwar's books, three times Bertha's books, and Cassey's books. Suitable for students in Grades 7-9.

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