To find the total number of students in the college, we need to follow these steps:
1. Determine the Number of Students More than 20 Years of Age:
We know the number of students who are exactly 20 years old is given as 42. The number of students more than 20 years of age is \(\frac{2}{3}\) of the number of students who are 20 years old:
[tex]\[
\text{Number of students more than 20 years of age} = \frac{2}{3} \times 42 = 28
\][/tex]
2. Calculate the Total Number of Students who are 20 Years or Older:
The total number of students who are 20 years or older includes both the students who are exactly 20 years old and the students who are more than 20 years old. Thus,
[tex]\[
\text{Number of students 20 years or older} = 42 + 28 = 70
\][/tex]
3. Use the Percentage of Students Less than 20 Years of Age to Find the Total Number of Students:
We are told that 63% of the students are less than 20 years old. This implies that 37% of the students are 20 years old or older. We can use this information to find the total number of students. Let \( N \) be the total number of students in the college. Then, using the information:
[tex]\[
37\% \text{ of the total number of students} = \text{Number of students 20 years or older}
\][/tex]
Mathematically, this can be expressed as:
[tex]\[
0.37 \times N = 70
\][/tex]
Solving for \( N \):
[tex]\[
N = \frac{70}{0.37} \approx 189.189189
\][/tex]
Therefore, the total number of students in the college is approximately 189.
