If `a/3 = b/4 = c/7` then `(a+b+c)/(c)` is equal to

Options

A. 7
B. 2
C. `1/2`
D. `7 1/7`

Answer

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

\[ \frac{a}{3} = \frac{b}{4} = \frac{c}{7} \]

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

1. From \( \frac{a}{3} = \lambda \), we can write:
\[ a = 3\lambda \]

2. From \( \frac{b}{4} = \lambda \), we can write:
\[ b = 4\lambda \]

3. From \( \frac{c}{7} = \lambda \), we can write:
\[ c = 7\lambda \]

Next, we need to find the expression \( \frac{a + b + c}{c} \):

4. Substitute \( a \), \( b \), and \( c \) into the expression:
\[ a + b + c = 3\lambda + 4\lambda + 7\lambda \]

5. Combine the terms:
\[ a + b + c = (3 + 4 + 7)\lambda = 14\lambda \]

Now, we can substitute this back into our expression:

6. The expression becomes:
\[ \frac{a + b + c}{c} = \frac{14\lambda}{7\lambda} \]

7. Simplify the fraction:
\[ \frac{14\lambda}{7\lambda} = \frac{14}{7} = 2 \]

Thus, the final answer is:

\[ \frac{a + b + c}{c} = 2 \]