If A:B=7:9 and B:C=3:5 then A:B:C is

Options

A. 7 : 9 : 5
B. 21 : 35 : 45
C. 7 : 9 : 15
D. 7 : 3 : 15

Answer

To solve the problem of finding the combined ratio A:B:C given the ratios A:B = 7:9 and B:C = 3:5, we can follow these steps:

### Step-by-Step Solution:

1. **Write down the given ratios**:
- A:B = 7:9
- B:C = 3:5

2. **Express the ratios in terms of a common variable**:
- Let A = 7x and B = 9x for some variable x (from the first ratio).
- Let B = 3y and C = 5y for some variable y (from the second ratio).

3. **Set the value of B from both ratios equal**:
- From the first ratio, B = 9x.
- From the second ratio, B = 3y.
- Therefore, we can set 9x = 3y.

4. **Solve for one variable in terms of the other**:
- Dividing both sides of the equation 9x = 3y by 3 gives us:
\[ 3x = y \quad \text{or} \quad y = 3x \]

5. **Substitute y back into the expressions for C**:
- Since C = 5y, substituting y gives us:
\[ C = 5(3x) = 15x \]

6. **Now we have all variables in terms of x**:
- A = 7x
- B = 9x
- C = 15x

7. **Write the combined ratio A:B:C**:
- Therefore, A:B:C = 7x : 9x : 15x.

8. **Simplify the ratio**:
- Since x is common in all terms, we can ignore it:
- A:B:C = 7 : 9 : 15.

### Final Answer:
A:B:C = 7:9:15.