If `a : b : c = 3 : 4 : 7`, then the ratio `(a + b + c): c` is equal to

Options

A. `2:1`
B. `14:3`
C. `7:2`
D. `1:2`

Answer

To solve the problem, we start with the given ratio \( a : b : c = 3 : 4 : 7 \).

### Step 1: Express \( a \), \( b \), and \( c \) in terms of a variable
We can express \( a \), \( b \), and \( c \) using a common variable \( x \):
\[ a = 3x, \quad b = 4x, \quad c = 7x \]

### Step 2: Calculate \( a + b + c \)
Now, we need to find the sum of \( a \), \( b \), and \( c \):
\[ a + b + c = 3x + 4x + 7x \]
\[ = (3 + 4 + 7)x = 14x \]

### Step 3: Set up the ratio \( (a + b + c) : c \)
We are asked to find the ratio \( (a + b + c) : c \):
\[ (a + b + c) : c = 14x : 7x \]

### Step 4: Simplify the ratio
To simplify the ratio \( 14x : 7x \), we can divide both terms by \( 7x \):
\[ = \frac{14x}{7x} : \frac{7x}{7x} = 2 : 1 \]

### Final Answer
Thus, the ratio \( (a + b + c) : c \) is equal to \( 2 : 1 \).

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