This question asks us to find the number of male teachers in University C based on the provided percentage distribution of teachers across six universities and the total number of teachers in University E.

First, let's look at the provided data:

We are given that the total number of teachers in University E is 1856. From the table, University E accounts for 29% of the total teachers across all six universities.

Calculating Total Teachers Across All Universities

We can find the total number of teachers by using the information for University E. Let the total number of teachers across all universities be \(T\).

We know that:

\(29\%\) of \(T\) = 1856

This can be written as:

\(0.29 \times T = 1856\)

To find \(T\), we divide the number of teachers in E by the percentage distribution for E (as a decimal):

\(T = \frac{1856}{0.29}\)

\(T = 6400\)

So, the total number of teachers across all six universities is 6400.

Finding the Number of Teachers in University C

Next, we need to find the total number of teachers in University C. According to the table, University C has 19% of the total teachers.

Number of teachers in University C = \(19\%\) of Total teachers

Number of teachers in University C = \(0.19 \times 6400\)

Number of teachers in University C = 1216

There are 1216 teachers in University C.

Determining the Number of Male Teachers in University C

We are told that 25% of the teachers in University C are females. This means the remaining percentage must be male teachers.

Percentage of male teachers in University C = \(100\%\) - Percentage of female teachers

Percentage of male teachers in University C = \(100\%\) - \(25\%\)

Percentage of male teachers in University C = \(75\%\)

Now, we can calculate the number of male teachers in University C:

Number of male teachers in University C = \(75\%\) of Total teachers in University C

Number of male teachers in University C = \(0.75 \times 1216\)

Number of male teachers in University C = 912

Therefore, the number of male teachers in University C is 912.

Summary of Steps

• Used the number of teachers in University E (1856) and its percentage (29%) to calculate the total number of teachers across all universities.
• Calculated the total number of teachers in University C using its percentage distribution (19%) and the total number of teachers.
• Determined the percentage of male teachers in University C (100% - 25% female = 75%).
• Calculated the number of male teachers in University C using the total teachers in C and the male percentage.

Revision Table: Key Calculations for Teachers

Additional Information: Percentage Concepts

Understanding percentages is key to solving problems like this. A percentage represents a part of a whole, expressed as a fraction of 100. For example, 29% means 29 out of 100, or \(\frac{29}{100}\) or 0.29 in decimal form.

When you have a percentage of a total and the value corresponding to that percentage, you can find the total using the formula:

\(\text{Total} = \frac{\text{Part}}{\text{Percentage as decimal}}\)

In this problem, we used the teachers in University E (1856) as the 'part' and 29% (0.29) as the 'percentage as decimal' to find the 'Total teachers'.

Similarly, to find a 'part' when you know the 'Total' and the 'Percentage', you use:

\(\text{Part} = \text{Total} \times \text{Percentage as decimal}\)

We used this to find the total teachers in University C and the number of male teachers in University C.