`(a)/(7)=(b)/(4)=(c )/(3)`, find `a:b:c=?`

Options

A. A) 1:1:1
B. B) 2:3:4
C. C) 7:4:3
D. D) 2:5:2

Answer

To solve the problem `(a)/(7) = (b)/(4) = (c)/(3)` and find the ratio `a:b:c`, we can follow these steps:

### Step 1: Set the common ratio
Let us denote the common ratio as `k`. Therefore, we can write:
\[ \frac{a}{7} = k, \quad \frac{b}{4} = k, \quad \frac{c}{3} = k \]

### Step 2: Express `a`, `b`, and `c` in terms of `k`
From the equations above, we can express `a`, `b`, and `c` as:
\[ a = 7k, \quad b = 4k, \quad c = 3k \]

### Step 3: Write the ratio `a:b:c`
Now, we can write the ratio `a:b:c` using the expressions we found:
\[ a:b:c = 7k : 4k : 3k \]

### Step 4: Simplify the ratio
Since `k` is a common factor in all terms, we can simplify the ratio by dividing each term by `k`:
\[ a:b:c = 7 : 4 : 3 \]

### Final Answer
Thus, the ratio `a:b:c` is:
\[ \boxed{7:4:3} \]

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