They won 3 out of every 4 home games and 2 out of every 3 away game. 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?
Let H be the number of home series
Let A be the number of away series
Let number of home wins = 3H
Let the number of home losses = 1H
Let the number of away wins = 2A
Let the numbe of away losses = 1A
And we know that
3H + 2A = 40 + 1H + 1A rearrange as
2H + A = 40 (1)
The number of home games = 4H
The number of away games = 3A
And we know that
4H = 3A
So
(4/3)H = A (2)
Sub (2) into (1) and we have that
2H + (4/3)H = 40
(10/3) H = 40 multiply both sides by 3/10
H = 40 (3/10)
H = 120 / 10
H = 12 = 12 home series
And
(4/3)H = A = (4/3)(12) = 16 away series
So....the total number of wins = 3H + 2A = 3(12) + 2(16) = 36 + 32 = 68 wins
And the total number of losses = 1H + 1A = 1(12) + 1(16) = 28 losses