A team of $8$ persons joins in a shooting competition. The best marksman scored $85$ points. If he had scored $92$ points, the average score for the team would have been $84$. The number of points, the team scored was

### Concept & Formula The total sum of observations is related to the average by the following baseline formula: $$ \text{Total Score} = \text{Average Score} \times \text{Number of Persons} $$ ### Step-by-Step Solution * **Given:** * Number of persons in the team = $8$ * Actual score of the best marksman = $85$ * Hypothetical score of the best marksman = $92$ * Hypothetical average score of the team = $84$ * **Calculation:** Let the actual total score of the team be $T$. If the marksman scores $92$ instead of $85$, the net increase in the team's total score would be: $$ 92 - 85 = 7 \text{ points} $$ Therefore, the hypothetical total score becomes $(T + 7)$. We are given that this hypothetical total score results in an average of $84$ for the $8$ members: $$ T + 7 = 84 \times 8 $$ $$ T + 7 = 672 $$ $$ T = 672 - 7 = 665 $$ ### Exam Strategy & Shortcut Calculate the hypothetical total directly: $84 \times 8 = 672$. Since this total is based on an assumed score that is $7$ points higher ($92 - 85 = 7$) than what was actually achieved, simply subtract the difference from the hypothetical total to find the actual score: $672 - 7 = 665$. ### Common Pitfall A common error is to accidentally add the $7$-point difference to $672$ instead of subtracting it, leading to the incorrect option of $672$ or a completely wrong value. Always remember that the hypothetical condition yields a *higher* total than reality. ### Final Answer **Therefore, the correct answer is 665.**