A:B = 5: 9 and B:C = 4:7 Find A:B : C.

Answer

To solve the problem of finding the ratio A:B:C given A:B = 5:9 and B:C = 4:7, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Given Ratios**:
- We have the ratio A:B = 5:9.
- We also have the ratio B:C = 4:7.

2. **Identify the Common Term**:
- The common term in both ratios is B. We need to make the value of B the same in both ratios to combine them.

3. **Find a Common Multiple for B**:
- The current values of B in the ratios are 9 (from A:B) and 4 (from B:C).
- The least common multiple (LCM) of 9 and 4 is 36.

4. **Adjust the Ratios**:
- To make B = 36, we need to scale the ratios:
- For A:B = 5:9, we multiply both parts by \( \frac{36}{9} = 4 \):
- A = 5 * 4 = 20
- B = 9 * 4 = 36
- For B:C = 4:7, we multiply both parts by \( \frac{36}{4} = 9 \):
- B = 4 * 9 = 36
- C = 7 * 9 = 63

5. **Combine the Ratios**:
- Now we have:
- A = 20
- B = 36
- C = 63
- Therefore, the combined ratio A:B:C is 20:36:63.

### Final Answer:
The ratio A:B:C is 20:36:63.

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