Understanding the Teacher Distribution in the University

The problem provides data about the distribution of 1600 teachers across six subjects (A-F) in a university. We are given the percentage of teachers in each subject and the ratio of male to female teachers within each subject. The question asks for the difference between the number of female teachers in Subject F and the number of male teachers in Subject C.

Analyzing the Teacher Data Table

Let's look at the information provided in the table for Subjects C and F.

Total number of teachers in the university is 1600.

Calculating Teachers in Subject C

First, we need to find the total number of teachers in Subject C.

• Percentage of teachers in Subject C = 12%
• Total teachers in the university = 1600
• Number of teachers in Subject C = 12% of 1600

Using the formula:

Number of teachers = (Percentage / 100) $\times$ Total teachers

Number of teachers in Subject C $= \left( \frac{12}{100} \right) \times 1600$

Number of teachers in Subject C $= 0.12 \times 1600 = 192$

So, there are 192 teachers in Subject C.

Finding Male Teachers in Subject C

The ratio of male to female teachers in Subject C is 1:3. This means for every 1 male teacher, there are 3 female teachers. The total number of parts in the ratio is $1 + 3 = 4$.

To find the number of male teachers, we divide the total teachers in Subject C by the sum of the ratio parts and multiply by the male part of the ratio.

• Total teachers in Subject C = 192
• Ratio of Male to Female = 1 : 3
• Sum of ratio parts = $1 + 3 = 4$

Number of male teachers in Subject C $= \left( \frac{\text{Male ratio part}}{\text{Sum of ratio parts}} \right) \times \text{Total teachers in C}$

Number of male teachers in Subject C $= \left( \frac{1}{4} \right) \times 192$

Number of male teachers in Subject C $= \frac{192}{4} = 48$

There are 48 male teachers in Subject C.

Calculating Teachers in Subject F

Next, we need to find the total number of teachers in Subject F.

• Percentage of teachers in Subject F = 22%
• Total teachers in the university = 1600
• Number of teachers in Subject F = 22% of 1600

Number of teachers in Subject F $= \left( \frac{22}{100} \right) \times 1600$

Number of teachers in Subject F $= 0.22 \times 1600 = 352$

So, there are 352 teachers in Subject F.

Finding Female Teachers in Subject F

The ratio of male to female teachers in Subject F is 7:9. The total number of parts in the ratio is $7 + 9 = 16$.

To find the number of female teachers, we divide the total teachers in Subject F by the sum of the ratio parts and multiply by the female part of the ratio.

• Total teachers in Subject F = 352
• Ratio of Male to Female = 7 : 9
• Sum of ratio parts = $7 + 9 = 16$

Number of female teachers in Subject F $= \left( \frac{\text{Female ratio part}}{\text{Sum of ratio parts}} \right) \times \text{Total teachers in F}$

Number of female teachers in Subject F $= \left( \frac{9}{16} \right) \times 352$

Number of female teachers in Subject F $= 9 \times \left( \frac{352}{16} \right)$

Number of female teachers in Subject F $= 9 \times 22 = 198$

There are 198 female teachers in Subject F.

Calculating the Difference

The question asks for the difference between the number of female teachers in Subject F and the number of male teachers in Subject C.

• Number of female teachers in Subject F = 198
• Number of male teachers in Subject C = 48

Difference = Number of female teachers in Subject F - Number of male teachers in Subject C

Difference $= 198 - 48 = 150$

The difference between the number of female teachers in Subject F and the number of male teachers in Subject C is 150.

Summary of Calculations

• Teachers in Subject C: $12\%$ of $1600 = 192$
• Male teachers in C: $\frac{1}{4}$ of $192 = 48$
• Teachers in Subject F: $22\%$ of $1600 = 352$
• Female teachers in F: $\frac{9}{16}$ of $352 = 198$
• Difference: $198 - 48 = 150$

Revision Table: Key Calculations for Teacher Distribution

Difference = Female teachers (F) - Male teachers (C) = $198 - 48 = 150$.

Additional Information: Percentage and Ratio Concepts

This problem combines two important concepts: percentages and ratios.

• Percentage: A percentage is a way of expressing a fraction out of 100. To find a percentage of a total number, you convert the percentage to a decimal or a fraction and multiply it by the total. For example, $12\%$ is equivalent to $\frac{12}{100}$ or $0.12$.
• Ratio: A ratio compares two or more quantities. For example, a ratio of 1:3 means that for every 1 part of the first quantity, there are 3 parts of the second quantity. The total number of parts is the sum of the numbers in the ratio ($1+3=4$). To distribute a total amount according to a ratio, you divide the total by the sum of the ratio parts and then multiply by each part of the ratio.

Data interpretation questions often require applying these basic mathematical concepts to information presented in tables, charts, or graphs. Practicing how to quickly calculate percentages and split amounts based on ratios is crucial for solving such problems efficiently.