Question

In a high school, the ratio of male to female students is 8:5. When 400 senior males to females are removed and 300 senior females are removed, the ration is 8:3. The number of students in the whole school is?

Answer 1

Males = 8X
Females = 5X

\[\frac{ 8X-400 }{ 5X-300 }= \frac{8}{3}\]
X = 75
Total = Males + Females = 8X + 5X = 13X = 13*75 = 975

Answer 2

Let's say there are x males and y females.
Then x/y = 8/5
When you remove the students, the ratio becomes:
(x - 400)/(y - 300) = 8/3
Cross multiply both equations:
5x = 8y
3(x - 400) = 8(y - 300)

5x = 8y
3x - 1200 = 8y - 2400

Now subtract bottom eq from top eq:

2x + 1200 = 2400
2x = 1200
x = 600

5x = 8y
5(600) = 8y
8y = 3000
y = 375

Answer: 600 males + 375 females = 975 students

Answer 3

let there be 8x and 5x males and females respectively
then by question we have (8x-400)/(5x-300)=8/3
or 8(x-50)/(5/(x-60)=8/3
or 3(x-50)=5(x-60)
3x-150=5x-300
2x =150
x=75
total number of students is 8x+5x=13x =13*75 =975