If `a/6=b/4=c/2` then` (a+b+c)/b=?`

Options

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

Answer

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

\[ \frac{a}{6} = \frac{b}{4} = \frac{c}{2} = k \]

where \( k \) is a constant.

### Step 1: Express \( a \), \( b \), and \( c \) in terms of \( k \)

From the equations, we can express \( a \), \( b \), and \( c \) as follows:

- For \( a \):
\[ a = 6k \]

- For \( b \):
\[ b = 4k \]

- For \( c \):
\[ c = 2k \]

### Step 2: Substitute \( a \), \( b \), and \( c \) into the expression \( \frac{a+b+c}{b} \)

Now we need to find \( \frac{a+b+c}{b} \):

\[ a + b + c = 6k + 4k + 2k \]

### Step 3: Simplify the numerator

Now we simplify the numerator:

\[ a + b + c = 6k + 4k + 2k = 12k \]

### Step 4: Substitute \( b \) into the expression

Now substitute \( b \) into the expression:

\[ \frac{a+b+c}{b} = \frac{12k}{4k} \]

### Step 5: Simplify the fraction

Now simplify the fraction:

\[ \frac{12k}{4k} = 3 \]

### Final Answer

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

\[ \boxed{3} \]

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