In an agricultural engineering college, the ratio of male students to female students was $5 : 3$. At the beginning of the semester, 50 male students graduated and left, while 50 female students newly enrolled, changing the ratio to $9 : 7$. The initial number of male students was ________ (answer in integer).
Answer Key:
500
Step-by-Step Solution & Explanation
Let the initial number of male students be $5x$ and female students be $3x$.
After the change:
$\frac{5x - 50}{3x + 50} = \frac{9}{7}$
$7(5x - 50) = 9(3x + 50)$
$35x - 350 = 27x + 450$
$35x - 27x = 450 + 350 \implies 8x = 800 \implies x = 100$
Initial number of male students $= 5x = 5(100) = 500$.