algebra
posted by Bryce on .
One half of the boys and onethird of the girls of Freemont High attended the homecoming game, wheras onethird of the boys and onehalf of the girls attended the homecoming dance. If there were 570 students at the game and 580 at the dance, then how many students are there at Freemont High?

b/2 + g/3 = 570 >3b+2g = 3420 (#1)
b/3 + g/2 = 580 >2b+3g = 3480 (#2)
#1 times 2 > 6b+4g = 6840
#2 times 3 > 6b+12g = 10440
subtract them:
8g = 3600
g = 450
back in #1:
3b + 900 = 3420
3b=2520
b=840
450 boys and 840 girls