Help in setting up equation

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helpinmath

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Apr 7, 2020
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Here is the question:
Teams in the girls' school basketball league are awarded 2 points for a win and 1 point for a loss. At the end of the season, Team A has 36 points and Team B has 24 points. Deborah, the league statistician, notices that the record of Team A is the reverse of the record of Team B: the number of Team A's wins equals the number of Team B's losses, while the number of Team A's losses equals the number of Team B's wins. What is the win-loss record of each team?

I know the answer is 16 wins 4 losses for Team A and 4 wins and 16 losses for Team B. How do I set up the equations to help me get this answer?
 
I would begin by writing:

[MATH]2W_A+L_A=36[/MATH]
[MATH]2W_B+L_B=24[/MATH]
[MATH]W_A=L_B[/MATH]
[MATH]W_B=L_A[/MATH]
And so the first two equations become:

[MATH]2W_A+W_B=36[/MATH]
[MATH]2W_B+W_A=24[/MATH]
Can you proceed?
 
The way I would proceed is the add and subtract the two equations (I last posted) to get:

[MATH]W_A+W_B=20[/MATH]
[MATH]W_A-W_B=12[/MATH]
Adding these, we ultimately get:

[MATH]W_A=16\implies W_B=4[/MATH]
 
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