SOLUTION: At the highschool 1/2 the boys and 1/3 of the girls attend homecoming game. 1/3 of the boys and 1/2 of the girls attended the homecoming dance. There were 570 students at the gam

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: At the highschool 1/2 the boys and 1/3 of the girls attend homecoming game. 1/3 of the boys and 1/2 of the girls attended the homecoming dance. There were 570 students at the gam      Log On


   

Question 131861: At the highschool 1/2 the boys and 1/3 of the girls attend homecoming game. 1/3 of the boys and 1/2 of the girls attended the homecoming dance. There were 570 students at the game and 580 students at the dance how many boys and girls attend the school.

Thanks for the help.
Answer by priya_2685(3) About Me  (Show Source):
You can put this solution on YOUR website!
let the no. of boys be x and the no. of girls be y
so, according to problem
1/2^x+ 1/3^y=570.....(1)
1/3^x+1/2^y= 580.....(2)

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 0.333333333333333*y to the right, we get:
0.5%2Ax+=+570+-+0.333333333333333%2Ay, or x+=+570%2F0.5+-+0.333333333333333%2Ay%2F0.5. Substitute that
into another equation:
0.333333333333333%2A%28570%2F0.5+-+0.333333333333333%2Ay%2F0.5%29+%2B+0.5%5Cy+=+580 and simplify: So, we know that y=720. Since x+=+570%2F0.5+-+0.333333333333333%2Ay%2F0.5, x=660.

Answer: system%28+x=660%2C+y=720+%29.


therefore, no. of boys= x= 660
no. of girls= y= 720