If P:Q = 2:9 and Q :R = 3:7, find P:R.

Answer

To solve the problem where \( P:Q = 2:9 \) and \( Q:R = 3:7 \), we need to find the ratio \( P:R \).

### Step-by-Step Solution:

1. **Write the Ratios in Fraction Form:**
- From the first ratio \( P:Q = 2:9 \), we can express it as:
\[ \frac{P}{Q} = \frac{2}{9} \]
- From the second ratio \( Q:R = 3:7 \), we can express it as:
\[ \frac{Q}{R} = \frac{3}{7} \]

2. **Express \( Q \) in terms of \( P \) and \( R \):**
- From the first ratio, we can express \( Q \) in terms of \( P \):
\[ Q = \frac{9}{2} P \]
- From the second ratio, we can express \( Q \) in terms of \( R \):
\[ Q = \frac{3}{7} R \]

3. **Set the two expressions for \( Q \) equal to each other:**
\[ \frac{9}{2} P = \frac{3}{7} R \]

4. **Cross-multiply to eliminate the fractions:**
\[ 9 \cdot 7 P = 3 \cdot 2 R \]
This simplifies to:
\[ 63P = 6R \]

5. **Rearrange to find the ratio \( P:R \):**
\[ \frac{P}{R} = \frac{6}{63} \]

6. **Simplify the ratio:**
\[ \frac{P}{R} = \frac{2}{21} \]

7. **Express the final answer in ratio form:**
\[ P:R = 2:21 \]

### Final Answer:
Thus, the ratio \( P:R \) is \( 2:21 \).