A Championship Season The Algenauts baseball team just finished a great year. During the season, they
won three out of every four of their home games and two out of every three of
their away games. All together they won 40 more games than they lost. If they
played as many home games as away games, what was their final record of
wins and losses?

If x = number of home games, x also = number of away games.

If they won 3/4 x at home, then they lost 1/4 x, and lost 1/3 x away for the same reason.  So your equation is

3/4 x + 2/3 x = 1/4 x + 1/3 x + 40

9/12 x + 8/12 x = 3/12 x + 4/12 x + 40

17/12 x = 7/12 x + 40

10/12 x = 40

so x = 40 ÷ 10/12 = 48

3/4 is 36, plus 2/3 is 32 so 68 wins and since 48+48 = 96, 96 - 68 losses

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