If `a/3 = b/4 = c/7` , then the value of `(a + b +c)/(c)` is

Options

A. `sqrt(3)`
B. `7`
C. `2`
D. `1/(sqrt7)`

Answer

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

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

Let us denote the common value of these fractions as \( k \). Therefore, we can express \( a \), \( b \), and \( c \) in terms of \( k \):

1. From \( \frac{a}{3} = k \), we have:
\[ a = 3k \]

2. From \( \frac{b}{4} = k \), we have:
\[ b = 4k \]

3. From \( \frac{c}{7} = k \), we have:
\[ c = 7k \]

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

4. Substitute the values of \( a \), \( b \), and \( c \):
\[ a + b + c = 3k + 4k + 7k \]

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

Now, we substitute \( c \) into the expression \( \frac{a + b + c}{c} \):

6. Substitute \( c = 7k \):
\[ \frac{a + b + c}{c} = \frac{14k}{7k} \]

7. Simplify the expression:
\[ \frac{14k}{7k} = 2 \]

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

\[ \boxed{2} \]