Question

A certain school has \[300\] students, \[142\] of whom are boys. It has \[30\] teachers, \[12\] of whom are men. What percent of the total number of students and teachers in the school is female?

Answer 1

Hint: To determine the number of girls in all students and a number of females in all teachers and sum them up. Then determine its percentage contribution from all students and teachers.
Given:
Total number of students\[ = 300\]
Total number of boys\[ = 142\]
Total number of teachers\[ = 30\]
Total number of men\[ = 12\]
To find: percentage of the total number of students and teachers in the school is female

Complete step-by-step solution:
Step 1: Determine total number of girls from the students
According to the question,
Total number of students\[ = 300\]
Total number of boys\[ = 142\]
Now, subtracting number of boys from total students gives total number of girls’ i.e.
Total number of girls = (total students)\[ - \](total boys)
Total number of girls \[ = 300 - 142\]\[ = 158\]
Hence, \[158\] girls are there in total students
Step 2: Determining total number of females from the teachers
According to the question,
Total number of teachers\[ = 30\]
Total number of men\[ = 12\]
Now, subtracting number of men from total number of teachers gives total number of females’ i.e.
Total number of females = (total number of teachers)\[ - \](total number of men)
Total number of females \[ = 30 - 12 = 18\]
Hence, there are total 18 females from all teachers
Step 3: determining percentage of the total number of students and teachers in the school is female
Total number of females from students and teachers = Total number of girls + Total number of female teachers
Total number of females from students and \[ = 158 + 18 = 176\]
Now as we know that,
Total number of students and teachers\[ = 300 + 30 = 330\]
Percentage of all females \[ = \dfrac{{176}}{{330}} \times 100\]
Percentage of all females \[ = \dfrac{160}{3}\% = 53.33\% \]
Hence, percentage of the total number of females from all students and teachers is equal to \[53.33\% \]

Note: Since girls are considered female, therefore the total number of females from students and teachers is given by adding the total number of girls from students and all female teachers. Percentage means a number or ratio expressed as a fraction of 100. percentage is unitless and dimensionless.