Final answer:
To find the total number of home and away games played, we need to use the given mean values of goals scored and create an equation. However, based on the equation, there seems to be a calculation error or missing details in the question.
Step-by-step explanation:
To find the total number of home and away games played, we need to determine the number of games played for each category. Let's assume there were x home games and y away games.
The mean number of goals scored is given as 2.5, so we can set up the equation: (2.5 * x + 1.8 * y) / (x + y). Since we want to find the total number of games played, we can also express this as x + y.
Combining these equations, we can solve for x + y using the given mean values.
In this case, (2.5 * x + 1.8 * y) / (x + y) = 2.5. By cross-multiplying, we have 2.5 * x + 1.8 * y = 2.5 * (x + y). Expanding this equation gives us 2.5 * x + 1.8 * y = 2.5 * x + 2.5 * y. Cancelling out the similar terms, we have 1.8 * y = 2.5 * y. Dividing both sides by 2.5, we get 1.8 = 2.5, which is not true. This implies that there is no solution for this scenario.
Therefore, it seems that there might be some calculation errors or missing details in the question.