A team of 8 shooters joins a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been
84. Determine the number of points, the team scored in the given competition?
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When a problem involves a hypothetical change to one data point, focus on how that change affects the total and the average. The change in total is the change in that data point.
Step 1: Understanding the Concept:
Average problems involve the relationship between individual changes and total score shifts. Step 2: Key Formula or Approach:
Total Score \( = \) Average \( \times \) Number of persons. Step 3: Detailed Explanation:
Let the actual total points be \( T \).
If the best marksman scored 92 instead of 85, the total would increase by \( 92 - 85 = 7 \) points.
New Total \( = T + 7 \).
Given new average is 84 for 8 shooters:
\( \frac{T + 7}{8} = 84 \)
\( T + 7 = 84 \cdot 8 = 672 \)
\( T = 672 - 7 = 665 \). Step 4: Final Answer:
The total score is 665.