A group of 300 mathematics teachers are classified into University Graduates, Diplomats, Specialists, and Others. We are given the number of teachers in the first three categories: 120, 90, and 50, respectively. Let $y$ represent the number of teachers in the "Others" category. The problem asks to calculate the value of $y$ and to draw a pie chart to illustrate the above information.

1. Problem Description

A group of 300 mathematics teachers are classified into University Graduates, Diplomats, Specialists, and Others. We are given the number of teachers in the first three categories: 120, 90, and 50, respectively. Let $y$ represent the number of teachers in the "Others" category. The problem asks to calculate the value of $y$ and to draw a pie chart to illustrate the above information.

2. Solution Steps

a. Calculate the value of $y$:

The total number of teachers is

3

0

0. The sum of teachers in each category must equal

3

0

0. Therefore, we can write the equation:

$120 + 90 + 50 + y = 300$

Combine the known values:

$260 + y = 300$

Subtract 260 from both sides to solve for $y$:

$y = 300 - 260$

$y = 40$

b. Draw a pie chart to illustrate the information:

To draw a pie chart, we need to calculate the angle for each category. The total angle in a circle is 360 degrees.

The angle for each category can be calculated by multiplying the fraction of each category to the total number of teachers, 300, and multiplying that by 360 degrees.

Angle = (Number of teachers in category / Total number of teachers) * 360

University Graduates:

$(120 / 300) * 360 = 0.4 * 360 = 144$ degrees

Diplomats:

$(90 / 300) * 360 = 0.3 * 360 = 108$ degrees

Specialists:

$(50 / 300) * 360 = (1/6) * 360 = 60$ degrees

Others:

$(40 / 300) * 360 = (2/15) * 360 = 48$ degrees

We can now draw the pie chart with the following angles:

University Graduates: 144 degrees

Diplomats: 108 degrees

Specialists: 60 degrees

Others: 48 degrees

3. Final Answer

The value of $y$ is

4

0. University Graduates: 144 degrees

Diplomats: 108 degrees

Specialists: 60 degrees

Others: 48 degrees