What is the fourth proportional to 24, 120 and 22?

Options

A. 110
B. 120
C. 100
D. 90

Answer

To find the fourth proportional to the numbers 24, 120, and 22, we can use the property of proportions. The fourth proportional \( x \) can be found using the formula:

\[ \frac{a}{b} = \frac{c}{x} \]

where \( a = 24 \), \( b = 120 \), and \( c = 22 \).

### Step-by-Step Solution:

1. **Set up the proportion**:
\[ \frac{24}{120} = \frac{22}{x} \]

2. **Cross-multiply**:
\[ 24 \cdot x = 120 \cdot 22 \]

3. **Calculate \( 120 \cdot 22 \)**:
\[ 120 \cdot 22 = 2640 \]

4. **Substitute back into the equation**:
\[ 24x = 2640 \]

5. **Solve for \( x \)**:
\[ x = \frac{2640}{24} \]

6. **Simplify \( \frac{2640}{24} \)**:
\[ x = 110 \]

Thus, the fourth proportional to 24, 120, and 22 is \( \boxed{110} \).