A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is ?

Options

A. A) 11
B. B) 7
C. C) 9
D. D) 13

Answer

To solve the problem, we need to find out how many revolutions the larger wheel makes when the smaller wheel, which has 6 cogs, makes 21 revolutions. The larger wheel has 14 cogs.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The number of revolutions of the two wheels is inversely proportional to the number of cogs they have. This means that as one wheel turns more, the other turns less.

2. **Set Up the Proportion**:
Let \( X \) be the number of revolutions made by the larger wheel. We can set up the proportion based on the number of cogs:
\[ \frac{6 \text{ cogs}}{14 \text{ cogs}} = \frac{X \text{ revolutions}}{21 \text{ revolutions}} \]

3. **Cross-Multiply**:
To solve for \( X \), we cross-multiply:
\[ 6 \times 21 = 14 \times X \]

4. **Calculate the Left Side**:
Calculate \( 6 \times 21 \):
\[ 6 \times 21 = 126 \]

5. **Set Up the Equation**:
Now we have:
\[ 126 = 14X \]

6. **Solve for \( X \)**:
Divide both sides by 14 to isolate \( X \):
\[ X = \frac{126}{14} \]

7. **Calculate \( X \)**:
Now calculate \( \frac{126}{14} \):
\[ X = 9 \]

### Final Answer:
The larger wheel makes **9 revolutions** when the smaller wheel makes 21 revolutions.

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