Sure! Let's go through Brenda's steps methodically to identify where the first mistake occurred.
### Step-by-Step Analysis:
Step 1: Find the total points needed to score in six games.
Brenda has 5 scores and wants an average score of 96 over 6 games.
To find the total points needed:
[tex]\[ \text{Total points needed} = \text{Desired average score} \times \text{Total number of games} \][/tex]
[tex]\[ = 96 \times 6 \][/tex]
[tex]\[ = 576 \][/tex]
So the correct total points needed for Brenda to achieve an average score of 96 over 6 games is 576.
However, Brenda's calculation was:
[tex]\[ 98 \times 8 - 578 \][/tex]
This calculation is incorrect both in terms of the formula used and the arithmetic. So, the first mistake occurs in Step 1.
Step 2: Find the total points scored.
Brenda needs to sum her first 5 scores:
[tex]\[ 92 + 110 + 85 + 78 + 96 \][/tex]
[tex]\[ = 461 \][/tex]
So, the correct total points scored in her first 5 games is 461.
Brenda's sum was:
[tex]\[ 92 + 110 + 85 + 78 - 365 \][/tex]
This is also incorrect. Brenda either added wrong values or somehow miscalculated. This could be seen as another mistake, but we have already identified the first mistake in Step 1.
Step 3: Subtract the total points scored from the total points needed.
After correctly computing Step 1 and Step 2, Brenda should:
[tex]\[ 576 - 461 \][/tex]
[tex]\[ = 115 \][/tex]
This gives the correct points Brenda needs to score in her next game to achieve her desired average.
Brenda's calculation was:
[tex]\[ 576 - 365 \][/tex]
Which gave her 211, incorrect due to previous mistakes.
Step 4: State the answer.
Finally, based on her previous calculations, Brenda incorrectly stated that:
[tex]\[ \text{She needs to score 211 in her next game.} \][/tex]
### Conclusion
Brenda made her first mistake in Step 1.
