If `a/3=b/4=c/5` then `(a+b+c)/b=?`

Options

A. 2
B. 3
C. 4
D. 5

Answer

To solve the problem, we need to find the value of \((a + b + c) / b\) given that \(\frac{a}{3} = \frac{b}{4} = \frac{c}{5}\).

### Step-by-Step Solution:

1. **Set a Common Variable**:
Let \(\frac{a}{3} = \frac{b}{4} = \frac{c}{5} = k\). This means:
\[ a = 3k, \quad b = 4k, \quad c = 5k \]

2. **Substitute Values**:
Now substitute \(a\), \(b\), and \(c\) into the expression \((a + b + c) / b\):
\[ a + b + c = 3k + 4k + 5k = 12k \]
Thus, we have:
\[ \frac{a + b + c}{b} = \frac{12k}{4k} \]

3. **Simplify the Expression**:
Simplifying the fraction:
\[ \frac{12k}{4k} = \frac{12}{4} = 3 \]

4. **Final Answer**:
Therefore, the value of \((a + b + c) / b\) is:
\[ \boxed{3} \]