17. The ages, in years, of the six members of a chess club are listed above. If the average of their ages is 14 years, what is the value of x?
Answer: A
x is 12 years.
To find the value of x, we can use the formula for the average. Since the average age of the six members is 14 years, the total age must equal 6 times 14, which is 84. By subtracting the known ages from 84, we can solve for x.
A) 12
This option is correct. If we set x to 12, the total age of the six members becomes 12 plus the sum of the other five ages. When calculated, this gives a total of 84, confirming that the average is indeed 14 years.
B) 13
This option is incorrect. If we assume x is 13, the total age would be 13 plus the sum of the other five ages. This would not sum to 84, resulting in an average greater than 14 years.
C) 14
This option is incorrect. Setting x to 14 would lead to a total age greater than 84 when combined with the other members' ages. This would yield an average exceeding 14 years, which contradicts the given information.
D) 15
This option is incorrect. If x equals 15, the total age would exceed 84 when adding the other five ages, leading to an average that is higher than 14 years. This does not satisfy the condition stated in the question.
Conclusion
The correct answer is 12 years because it allows the total age of the club members to equal 84, thus maintaining the average of 14 years. All other options result in total ages that would exceed or fall short of this value, demonstrating that they do not meet the average requirement.