Question

One half of the boys and one-third of the girls of Freemont High attended the homecoming game, wheras one-third of the boys and one-half 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?

Answer 1

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