Girl bet me i couldnt find the awnser to this math problem

Question

The number of pupils in school A is equal to half the number of pupils in school B. The ratio of the boys in school A and the boys in school B is 1:3 and the ratio of the girls in school A and the girls in school B is 3:5. The number of boys in school B is 200 higher than the number of boys in school A. Find the number of boys and girls in each school.

Answer 1

Xa = # of boys in school A
Xb = # of boys in school B
Ya = # of girls in school A
Yb = # of girls in school B

There are half as many students in school A as in school B:
(Xa + Ya )*2 = Xb + Yb

2*Xa + 2*Ya = Xb + Yb <--- equation #1

The ratio of boys between school A and School B is 1 to 3.

Xa + 3*Xb = Xa + Xb

3*Xb = Xb

2*Xb = 0

Xb = 0 <--- equation #2


The ratio of girls between school A and School B is 3 to 5.


3*Ya + 5*Yb = Ya + Yb
2*Ya + 4 * Yb = 0
Ya + 2*Yb = 0
Ya = -2*Yb <--- equation #3


There are 200 more boys in school B than in school A.
Xa + 200 = Xb <--- equation #4


Since Xb=0 per equation #2, Xa + 200 = 0
Xa = -200

Substituting these values into equation #1:

2*(-200) + 2*Ya = 0 + Yb

2*Ya - 400 = Yb <--- call this equation ALPHA.

Substituting equation #3 into equation ALPHA:
2*(-2*Yb) - 400 = Yb
-4*Yb - 400 = Yb
-400 = 5*Yb
Yb = -80

Ya = -2*-80 = 160

There are -200 boys in school A
There are zero boys in school B
There are 160 girls in school A
There are -80 girls in school B.

School A has -200 + 160 = -40 students
School B has 0 + -80 students.
So yes there are half as many students in school A as in school B since half of -80 is -40.

There are -200 total boys.
The ratio of boys between the two schools is -200/-200 = 1 and 0/200 = 0
So yes, 1*-200 + 3 * 0 = -200 + 0 = -200 which is the 3 to 1 ratio.

There are 80 total girls.
The ratio of girls between the two schools is 160/80 = 2 and -80/80 = -1.
So yes, 3*160 + 5*-80 = 480 - 400 = 80 which is the 3 to 5 ratio.

I do believe she owes you some money
because this problem is SO FLAWED!
Perhaps call the bet off, and declare it NULL and VOID