Question

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?

• A. 588
• B. 555
• C. 672
• D. 645
• E. 665

Hint:

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.

Answer 1

Answer: (E)

Step 1: Define Variables:
Let the total score of the team in the actual competition be $S$. The best marksman scored 85 points.
Step 2: Use the Hypothetical Scenario:
If the best marksman had scored 92 instead of 85, the new total would be $S + (92-85) = S + 7$. The average in this scenario is given as 84 for the team of 8. So, $\frac{S+7}{8} = 84$.
Step 3: Solve for $S$:
$S+7 = 84 \times 8 = 672$. $S = 672 - 7 = 665$.
Step 4: Final Answer:
The total points scored by the team is 665.