M04-04

x = number of female
number of male = 100-x
combining 1,2. we get the equation 0.05X/ 0.12(100-x)+0.05X

is this equation not enough?

No. Firstly, we don't know whether there are 100 students in total, so it is incorrect to assume that if x represents the number of females, then the number of males is 100 - x.

Instead, let's assume that there are n students in total, with f representing the percentage of females and 1 - f representing the percentage of males. Then, we can calculate the percentage of females in math courses as:

\(\frac{0.05fn}{0.12(1 - f)n + 0.05fn}\)

Simplifying this expression by reducing by n gives:

\(\frac{0.05f}{0.12(1 - f) + 0.05f} \)

If f is close to 1 (100%), this expression approaches 1, indicating that the percentage of females in math courses is almost 100%. Similarly, if f is close to 0 (0%), the expression approaches 0, indicating that the percentage of females in math courses is almost 0%.

Note that the percentage of females in math courses does not depend on the total number of students in the university, but rather on the ratio of males to females in the university.

However, it is important to note that the algebraic calculations above are not necessary and can be avoided if one thinks logically before jumping to algebra, as demonstrated in the official solution.

sorry I meant 100%, not 100. so x is the total percentage of females out of the 100% number of students.

huge thank you for this clarification, I understand now why we can't answer this question.