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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