If `A: B = 7 : 9` and `B : C = 3 : 5`, then `A: B : C` is equal to

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 ratio \( A : B : C \) given \( A : B = 7 : 9 \) and \( B : C = 3 : 5 \), we can follow these steps:

### Step-by-Step Solution:

1. **Write down the given ratios:**
- We have \( A : B = 7 : 9 \) and \( B : C = 3 : 5 \).

2. **Express the ratios in terms of a common variable:**
- Let \( A = 7x \) and \( B = 9x \) for some variable \( x \).
- For the second ratio \( B : C = 3 : 5 \), we can express \( B \) in terms of another variable. Let \( B = 3y \) and \( C = 5y \) for some variable \( y \).

3. **Find a common value for \( B \):**
- From the first ratio, we have \( B = 9x \).
- From the second ratio, we have \( B = 3y \).
- Set these two expressions for \( B \) equal to each other:
\[ 9x = 3y \]
- Solve for \( y \) in terms of \( x \):
\[ y = 3x \]

4. **Substitute \( y \) back to find \( C \):**
- Substitute \( y = 3x \) into \( C = 5y \):
\[ C = 5(3x) = 15x \]

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

6. **Write the combined ratio \( A : B : C \):**
- Therefore, \( A : B : C = 7x : 9x : 15x \).
- Since \( x \) is common in all terms, we can simplify it to:
\[ A : B : C = 7 : 9 : 15 \]

### Final Answer:
Thus, the ratio \( A : B : C \) is \( 7 : 9 : 15 \).

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