This problem asks for the ratio of the number of male teachers in City C to the number of female teachers in City B, based on the provided table data.

Understanding the Data Table

The table provides two key pieces of information for each city:

• The percentage distribution of the total teachers across the six cities.
• The exact number of male teachers in each city.

The total number of teachers across all six cities is given as 4500.

Step-by-Step Solution: Calculating the Ratio

We need to find two values to determine the ratio:

1. Number of male teachers in City C.
2. Number of female teachers in City B.

1. Number of Male Teachers in City C

The table directly gives the number of male teachers in City C.

Number of male teachers in City C = 600.

2. Number of Female Teachers in City B

To find the number of female teachers in City B, we first need the total number of teachers in City B. We can calculate this using the total number of teachers and the percentage distribution for City B.

• Total number of teachers = 4500
• Percentage of teachers in City B = 16%

Total teachers in City B can be calculated as:

Total teachers in City B $= \left(\frac{\text{Percentage of teachers in City B}}{100}\right) \times \text{Total number of teachers}$

Total teachers in City B $= \left(\frac{16}{100}\right) \times 4500$

Total teachers in City B $= 0.16 \times 4500$

Total teachers in City B $= 720$

Now that we have the total teachers in City B and the number of male teachers in City B (from the table), we can find the number of female teachers.

• Total teachers in City B = 720
• Number of male teachers in City B = 400 (from table)

Number of female teachers in City B = Total teachers in City B - Number of male teachers in City B

Number of female teachers in City B = $720 - 400$

Number of female teachers in City B = $320$

3. Calculating the Ratio

We need the ratio of the number of male teachers in City C to the number of female teachers in City B.

Ratio = (Number of male teachers in City C) : (Number of female teachers in City B)

Ratio = $600 : 320$

To simplify the ratio, we can divide both numbers by their greatest common divisor. We can start by dividing by common factors like 10, then 2, etc.

$600 : 320 \rightarrow \frac{600}{10} : \frac{320}{10} \rightarrow 60 : 32$

Now, divide by 4:

$60 : 32 \rightarrow \frac{60}{4} : \frac{32}{4} \rightarrow 15 : 8$

The simplified ratio is 15 : 8.

Comparing with Options

Let's look at the given options:

1. 11 ∶ 15
2. 15 ∶ 11
3. 15 ∶  8
4. 8 ∶  15

Our calculated ratio, 15 : 8, matches option 3.

Conclusion

The ratio of the number of male teachers in City C to the number of female teachers in City B is 15 ∶ 8.

Revision Table: Teacher Distribution Analysis

From the table:

• Male teachers in City C = 600
• Female teachers in City B = 320

Ratio = $600 : 320 = 15 : 8$. This confirms our earlier calculation.

Additional Information: Understanding Ratios

A ratio is a way to compare two quantities. It shows how many times one quantity is contained within another or how the two quantities relate to each other. Ratios can be written in a few ways:

• Using a colon, like $a : b$.
• As a fraction, like $\frac{a}{b}$.

When dealing with ratios, it's standard practice to simplify them to their lowest terms by dividing both parts by their greatest common divisor. In this problem, the ratio $600 : 320$ was simplified to $15 : 8$ by dividing both numbers by 40.

Ratios are dimensionless quantities, meaning they do not have units, as they represent a comparison between two quantities of the same type (in this case, numbers of teachers).