# algebra

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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?

• algebra -

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

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