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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?

 Jan 16, 2020
 #1
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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

 

 

cool cool cool

 Jan 16, 2020

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