Final answer:
After setting up an equation based on the total points scored by both teams and the number of games each played, it's determined that the Aggies scored 50 points per game. However, this solution doesn't match any of the provided multiple-choice options, indicating a possible error in the question or the options.
Step-by-step explanation:
We need to figure out how many points the Aggies scored each game by solving the equation that arises from the information given. Let's let x be the average points the Aggies score each game. According to the problem, the Longhorns score 30 points less than the Aggies in a game, which can be represented as x-30.
Now, since the Longhorns have 12 games and the Aggies have 13 games, the total points scored by the Longhorns in a season will be 12*(x-30) and for the Aggies, it will be 13*x. The sum of these two should equal the total points scored by both teams, 890 points.
Putting this all into an equation, we get:
12*(x-30) + 13*x = 890
Now we will solve the equation step-by-step:
- Multiply out the brackets: 12x - 360 + 13x = 890
- Combine like terms: 25x - 360 = 890
- Add 360 to both sides: 25x = 1250
- Divide both sides by 25: x = 50
Thus, the Aggies scored 50 points per game, which means the Longhorns, scoring 30 less, would be at 20 points per game. However, none of the options given in the multiple choice (65, 70, 75, or 80 points) match the solution of 50 points that we calculated for the average points the Aggies scored each game. There may be an error in the question or the options provided.