A group of 300 mathematics teachers are classified into four categories: University Graduates (120), Diplomats (90), Specialists (50), and Others (y). We need to find the value of y, draw a pie chart to represent the data, and find the fraction of teachers who are specialists.

1. Problem Description

A group of 300 mathematics teachers are classified into four categories: University Graduates (120), Diplomats (90), Specialists (50), and Others (y). We need to find the value of y, draw a pie chart to represent the data, and find the fraction of teachers who are specialists.

2. Solution Steps

a. Calculate the value of y:

The total number of teachers is

3

0

0. Therefore, the sum of teachers in each category must equal

3

0

0. $120 + 90 + 50 + y = 300$

$260 + y = 300$

$y = 300 - 260$

$y = 40$

b. Draw a pie chart to illustrate the above information:

To draw a pie chart, we need to calculate the angle for each category. The total angle in a circle is $360^{\circ}$. We calculate the angle for each category by multiplying the fraction of teachers in that category by $360^{\circ}$.

University Graduates:

Fraction = $\frac{120}{300} = \frac{2}{5}$

Angle = $\frac{2}{5} \times 360^{\circ} = 144^{\circ}$

Diplomats:

Fraction = $\frac{90}{300} = \frac{3}{10}$

Angle = $\frac{3}{10} \times 360^{\circ} = 108^{\circ}$

Specialists:

Fraction = $\frac{50}{300} = \frac{1}{6}$

Angle = $\frac{1}{6} \times 360^{\circ} = 60^{\circ}$

Others:

Fraction = $\frac{40}{300} = \frac{2}{15}$

Angle = $\frac{2}{15} \times 360^{\circ} = 48^{\circ}$

c. What fraction of the teachers are specialists?

The number of specialists is 50, and the total number of teachers is

3

0

0. Fraction = $\frac{50}{300} = \frac{1}{6}$

3. Final Answer

a. The value of y is

4

0. b. The pie chart would have the following angles: University Graduates ($144^{\circ}$), Diplomats ($108^{\circ}$), Specialists ($60^{\circ}$), and Others ($48^{\circ}$).

c. The fraction of teachers who are specialists is $\frac{1}{6}$.