If A/2 = B/5 = C/7, then what is A : B : C?

Options

A. `2 : 5 : 7 `
B. `2 : 5 : 12 `
C. ` 5 : 2 : 7 `
D. `7 : 5 : 2 `

Answer

To solve the problem, we need to find the ratio A : B : C given that A/2 = B/5 = C/7.

### Step-by-step Solution:

1. **Set a Common Variable**:
Let A/2 = B/5 = C/7 = k (where k is a constant).

2. **Express A, B, and C in terms of k**:
- From A/2 = k, we can express A as:
\[ A = 2k \]
- From B/5 = k, we can express B as:
\[ B = 5k \]
- From C/7 = k, we can express C as:
\[ C = 7k \]

3. **Write the Ratio A : B : C**:
Now, we can write the ratio A : B : C using the expressions we found:
\[ A : B : C = 2k : 5k : 7k \]

4. **Simplify the Ratio**:
Since k is common in all three terms, we can divide each term by k:
\[ A : B : C = 2 : 5 : 7 \]

### Final Answer:
The ratio A : B : C is **2 : 5 : 7**.

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