Sure, let's work through this step-by-step to find out how many points Ivan needs to score in his next game to achieve an average of 24 points per game.
1. Identify the scores in the first four games:
- Game 1: 16 points
- Game 2: 24 points
- Game 3: 20 points
- Game 4: 30 points
2. Determine the desired average:
- The desired average score is 24 points per game.
3. Identify the total number of games including the next game:
- Number of games = 5 (4 games already played + 1 next game)
4. Calculate the total points needed for the desired average:
- To find out the total points Ivan needs to accumulate over 5 games to have an average of 24 points per game, we use the formula for the average:
[tex]\[
\text{Desired average} = \frac{\text{Total points}}{\text{Number of games}}
\][/tex]
Rearranging for total points:
[tex]\[
\text{Total points needed} = \text{Desired average} \times \text{Number of games}
\][/tex]
So:
[tex]\[
\text{Total points needed} = 24 \times 5 = 120
\][/tex]
5. Calculate the total points scored in the first four games:
- Add the points scored in the first four games:
[tex]\[
\text{Current total points} = 16 + 24 + 20 + 30 = 90
\][/tex]
6. Determine the points needed in the next game:
- To find out how many points Ivan needs to score in his next game, subtract the total points scored in the first four games from the total points needed:
[tex]\[
\text{Points needed} = \text{Total points needed} - \text{Current total points}
\][/tex]
So:
[tex]\[
\text{Points needed} = 120 - 90 = 30
\][/tex]
Conclusion: Ivan needs to score 30 points in his next game to achieve an average of 24 points per game over the 5 games.
