Understanding University Teacher Distribution Data

The problem provides a table showing the percentage distribution of teachers across six different universities (A, B, C, D, E, F). We are given that the total number of teachers specifically in University E is 1856. We need to find the number of teachers in University B and express it as an approximate percentage of the combined number of teachers in University D and University E.

Step-by-Step Calculation for University Teacher Distribution

Let's break down the calculation into several clear steps to find the required percentage.

Step 1: Find the Total Number of Teachers

We know the number of teachers in University E is 1856, and this represents 29% of the total number of teachers across all universities. We can use this information to find the total number of teachers.

• Let \( T \) be the total number of teachers in all six universities.
• Teachers in University E = 29% of \( T \).
• So, \( 1856 = 29\% \text{ of } T \)
• \( 1856 = \frac{29}{100} \times T \)
• To find \( T \), we rearrange the equation:
• \( T = \frac{1856 \times 100}{29} \)
• \( T = \frac{185600}{29} \)
• \( T = 6400 \)

The total number of teachers in all six universities is 6400.

Step 2: Find the Number of Teachers in University B

University B has 17% of the total number of teachers. We can calculate the number of teachers in University B using the total number of teachers we just found.

• Teachers in University B = 17% of Total Teachers
• Teachers in University B = \( \frac{17}{100} \times 6400 \)
• Teachers in University B = \( 0.17 \times 6400 \)
• Teachers in University B = 1088

There are 1088 teachers in University B.

Step 3: Find the Number of Teachers in University D

University D has 6% of the total number of teachers. We calculate the number of teachers in University D similarly.

• Teachers in University D = 6% of Total Teachers
• Teachers in University D = \( \frac{6}{100} \times 6400 \)
• Teachers in University D = \( 0.06 \times 6400 \)
• Teachers in University D = 384

There are 384 teachers in University D.

Step 4: Find the Combined Number of Teachers in University D and University E

We need the sum of teachers in University D and University E.

• Teachers in University D = 384
• Teachers in University E = 1856 (given)
• Combined teachers in D and E = Teachers in D + Teachers in E
• Combined teachers in D and E = 384 + 1856
• Combined teachers in D and E = 2240

There are 2240 teachers in University D and University E together.

Step 5: Calculate the Percentage of Teachers in B relative to the Combined Teachers in D and E

Now we calculate the number of teachers in University B as a percentage of the combined number of teachers in D and E.

• Percentage = \( \left( \frac{\text{Teachers in University B}}{\text{Combined teachers in D and E}} \right) \times 100 \)
• Percentage = \( \left( \frac{1088}{2240} \right) \times 100 \)
• Percentage = \( 0.485714... \times 100 \)
• Percentage \( \approx 48.57\% \)

Step 6: Approximate the Percentage

The question asks for the approximate percentage. Rounding 48.57% to the nearest whole number gives 49%.

The number of teachers in University B is approximately 49% of the total number of teachers in University D and University E together.

Revision Table: Key Data Points and Calculations

Additional Information on Percentage Calculations

Percentage is a way of expressing a proportion of a whole, with the whole being considered as 100. The symbol '%' means 'out of 100'.

• To convert a percentage to a decimal: Divide the percentage by 100. For example, 29% = \(29/100 = 0.29\).
• To find a percentage of a number: Convert the percentage to a decimal (or fraction) and multiply by the number. For example, 17% of 6400 = \(0.17 \times 6400\).
• To find what percentage one number is of another: Divide the first number by the second number (the whole) and multiply by 100. For example, to find what percentage 1088 is of 2240, calculate \((1088 / 2240) \times 100\).
• In data interpretation problems involving percentages, if you know the value of a certain percentage, you can find the total value (100%) by setting up a proportion or using the formula: \( \text{Total} = \frac{\text{Part Value}}{\text{Percentage as Decimal}} \).

Understanding how to work with percentages and how to calculate parts of a whole or express one part as a proportion of another part or the whole is crucial for solving data interpretation questions based on percentages and distributions.