If `a/2 = b/3 = c/4`, then what is the value of `(a+b+c)/b` ?

Options

A. 3
B. 2
C. `4/3`
D. `7/3`

Answer

To solve the problem, we start with the given equation:

\[ \frac{a}{2} = \frac{b}{3} = \frac{c}{4} \]

Let's denote this common ratio as \( k \). Therefore, we can express \( a \), \( b \), and \( c \) in terms of \( k \):

1. From \( \frac{a}{2} = k \), we get:
\[ a = 2k \]

2. From \( \frac{b}{3} = k \), we get:
\[ b = 3k \]

3. From \( \frac{c}{4} = k \), we get:
\[ c = 4k \]

Now, we need to find the value of \( \frac{a + b + c}{b} \).

4. First, we calculate \( a + b + c \):
\[ a + b + c = 2k + 3k + 4k = 9k \]

5. Now, we substitute \( b \) into the expression:
\[ b = 3k \]

6. Therefore, we can write:
\[ \frac{a + b + c}{b} = \frac{9k}{3k} \]

7. Simplifying this gives:
\[ \frac{9k}{3k} = 3 \]

Thus, the value of \( \frac{a + b + c}{b} \) is \( 3 \).

### Final Answer:
\[ \frac{a + b + c}{b} = 3 \]