the cougars basket ball team played two games against the bobcats. in the games, the cougars scored a totoal of 96 points and the bobcats scored a total of 89 points.
1. write possible scores for both games showing the cougars winning.
2. write possible scores for both games showing the cougars losing one game
To find the possible scores for both games, we can set up a system of equations based on the information given.
Let's assume the Cougars' scores for the two games are represented by variables x and y, and the Bobcats' scores are represented by variables a and b.
1. Possible scores for both games with the Cougars winning:
Since the Cougars won both games, their total points (x + y) must be greater than the Bobcats' total points (a + b).
x + y > a + b
Substituting the given information that the Cougars scored a total of 96 points and the Bobcats scored a total of 89 points:
x + y > 89
Since we want to find possible scores, we need to assign specific values to the variables. Here are some examples:
- If x = 50 and y = 46, the Cougars' total points would be 96, and this would satisfy the condition (50 + 46 > 89). So, one possible set of scores could be Cougars 50, Bobcats 39.
- If x = 20 and y = 70, the Cougars' total points would be 90, and this would also satisfy the condition (20 + 70 > 89). So, another possible set of scores could be Cougars 20, Bobcats 69.
Remember, there are multiple possible combinations of scores that would satisfy this condition.
2. Possible scores for both games with the Cougars losing one game:
This time, we know that the Cougars lost one game, so their total points (x + y) must be less than the Bobcats' total points (a + b).
x + y < a + b
Using the given information:
x + y < 96
Again, let's assign specific values to the variables to find possible scores:
- If x = 75 and y = 5, the Cougars' total points would be 80, and this would be less than the Bobcats' total points (75 + 5 < 89). So, one possible set of scores could be Cougars 75, Bobcats 14.
- If x = 40 and y = 50, the Cougars' total points would be 90, but this would be greater than the Bobcats' total points (40 + 50 > 89). Therefore, this combination does not satisfy the conditions for the Cougars losing one game.
It's important to note that there can be multiple valid combinations of scores, so these are just examples to help you understand the process.