Question
Milan has scored 20, 25, 29, and points in his four basketball games so far. How many points does he need to score in his next game so that his average (mean) is points per game?
Answers
GPT-4o mini
To find out how many points Milan needs to score in his next game to achieve a specific average, we can follow these steps:
1. **Determine the total points scored so far**:
The points scored in the four games are 20, 25, 29, and the fourth game's points is undetermined, let's denote it as \( x \). So,
\[
\text{Total points} = 20 + 25 + 29 + x = 74 + x
\]
2. **Set up the equation for the average with the next game's points**:
Let \( y \) be the points Milan scores in the next game. Thus, the total points after five games will be \( 74 + x + y \), and the total number of games will be 5. The average should equal the desired average \( A \):
\[
\frac{74 + x + y}{5} = A
\]
3. **Clear the fraction by multiplying both sides by 5**:
\[
74 + x + y = 5A
\]
4. **Rearrange to find \( y \)**:
From the equation, we can express \( y \) as follows:
\[
y = 5A - 74 - x
\]
Now, we need to know what \( x \) and \( A \) are to find an explicit number for \( y \). Without the specified average \( A \) or the score of the fourth game, we cannot give a numerical answer.
Assuming you meant to find an unspecified score for \( x \) or a specified score for the average, please provide either \( A \) (the average you want to reach) or perhaps clarify the score of the fourth game.
1. **Determine the total points scored so far**:
The points scored in the four games are 20, 25, 29, and the fourth game's points is undetermined, let's denote it as \( x \). So,
\[
\text{Total points} = 20 + 25 + 29 + x = 74 + x
\]
2. **Set up the equation for the average with the next game's points**:
Let \( y \) be the points Milan scores in the next game. Thus, the total points after five games will be \( 74 + x + y \), and the total number of games will be 5. The average should equal the desired average \( A \):
\[
\frac{74 + x + y}{5} = A
\]
3. **Clear the fraction by multiplying both sides by 5**:
\[
74 + x + y = 5A
\]
4. **Rearrange to find \( y \)**:
From the equation, we can express \( y \) as follows:
\[
y = 5A - 74 - x
\]
Now, we need to know what \( x \) and \( A \) are to find an explicit number for \( y \). Without the specified average \( A \) or the score of the fourth game, we cannot give a numerical answer.
Assuming you meant to find an unspecified score for \( x \) or a specified score for the average, please provide either \( A \) (the average you want to reach) or perhaps clarify the score of the fourth game.