To find the value of \( A + B + C \), let's use the values of \( A \) and \( B \) we previously calculated:

### Given:
1. \( \frac{A}{C} = \frac{1}{2} \)
2. \( \frac{B}{C} = \frac{3}{5} \)

### Step 1: Express \( A \) and \( B \) in terms of \( C \):
- From \( \frac{A}{C} = \frac{1}{2} \), we have \( A = \frac{C}{2} \).
- From \( \frac{B}{C} = \frac{3}{5} \), we have \( B = \frac{3C}{5} \).

### Step 2: Calculate \( A + B + C \):
\[
A + B + C = \frac{C}{2} + \frac{3C}{5} + C
\]

### Step 3: Combine the fractions:
To add \( \frac{C}{2} \) and \( \frac{3C}{5} \), we need a common denominator. The least common denominator between 2 and 5 is 10.

\[
\frac{C}{2} = \frac{5C}{10}, \quad \frac{3C}{5} = \frac{6C}{10}
\]
So,
\[
A + B = \frac{5C}{10} + \frac{6C}{10} = \frac{11C}{10}
\]

Now, add \( C \) (which is \( \frac{10C}{10} \)):

\[
A + B + C = \frac{11C}{10} + \frac{10C}{10} = \frac{21C}{10}
\]

### Final Answer:
The value of \( A + B + C \) is \( \frac{21C}{10} \).

Would you like further clarification or have any other questions?

### Related Questions:
1. What is the value of \( A + B + C \) if \( C = 10 \)?
2. How would \( A + B + C \) change if the initial conditions were different?
3. Can you find the numerical value of \( A + B + C \) if \( C \) is known?
4. What happens to the sum \( A + B + C \) if \( C \) is negative?
5. What does \( A + B + C \) represent in the context of this problem?

### Tip:
When working with algebraic expressions involving fractions, always simplify the fractions first before performing operations to avoid unnecessary complexity.

Learn how to find the value of A + B + C using fractional equations. This problem involves algebraic manipulation with fractions and is suitable for students in Grades 7-9. Explore step-by-step solutions and related questions.

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