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?
x = 12
To find the value of x, we can use the formula for the average, which is the sum of the ages divided by the number of members. Given that the average age is 14 and there are six members, we can set up the equation to solve for x.
If x = 12, the total sum of the ages would be 12 + 14 + 14 + 14 + 14 + 14 = 72. The average is then calculated as 72 ÷ 6 = 12, which is incorrect. Therefore, this option does not satisfy the condition of the average being 14.
If x = 13, the total sum of the ages would be 13 + 14 + 14 + 14 + 14 + 14 = 73. The average is calculated as 73 ÷ 6 = 12.17, which is not equal to 14. Thus, this option also does not meet the average requirement.
If x = 14, the total sum of the ages would be 14 + 14 + 14 + 14 + 14 + 14 = 84. The average is calculated as 84 ÷ 6 = 14, which matches the required average. However, this is not the minimum value of x that still meets the average.
If x = 15, the total sum of the ages would be 15 + 14 + 14 + 14 + 14 + 14 = 85. The average is calculated as 85 ÷ 6 = 14.17, which exceeds the required average. Therefore, this option is also invalid.
To achieve an average age of 14 years among the six members of the chess club, the value of x must be 12, as it allows the total age to meet the average needed. All other options either do not meet the average or exceed it, confirming that x = 12 is the only valid solution.
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