Find x for which the number are in proportion.
a. `45, 81, x, 99`
b. `66, x, 72,132`

Answer

To solve the problem of finding \( x \) for which the numbers are in proportion, we will use the property of proportions that states:

If \( a, b, c, d \) are in proportion, then \( a \times d = b \times c \).

Let's solve the two parts step by step:

### Part a: \( 45, 81, x, 99 \)

1. **Identify the numbers**: Here, \( a = 45 \), \( b = 81 \), \( c = x \), and \( d = 99 \).

2. **Set up the proportion**: According to the rule, we have:
\[ 45 \times 99 = 81 \times x \]

3. **Calculate \( 45 \times 99 \)**:
\[ 45 \times 99 = 4455 \]

4. **Set up the equation**:
\[ 4455 = 81 \times x \]

5. **Solve for \( x \)**:
\[ x = \frac{4455}{81} \]

6. **Calculate \( x \)**:
\[ x = 55 \]

### Part b: \( 66, x, 72, 132 \)

1. **Identify the numbers**: Here, \( a = 66 \), \( b = x \), \( c = 72 \), and \( d = 132 \).

2. **Set up the proportion**: According to the rule, we have:
\[ 66 \times 132 = x \times 72 \]

3. **Calculate \( 66 \times 132 \)**:
\[ 66 \times 132 = 8712 \]

4. **Set up the equation**:
\[ 8712 = x \times 72 \]

5. **Solve for \( x \)**:
\[ x = \frac{8712}{72} \]

6. **Calculate \( x \)**:
\[ x = 121 \]

### Final Answers:
- For part a, \( x = 55 \)
- For part b, \( x = 121 \)

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