Question 31

If the average of 5, 13, 18, 20, 22, $$K$$ and $$K + 6$$ is 16, then find the value of $$K$$.

Solution

There are 7 numbers with average 16, so their sum is $$7 \times 16 = 112$$. The sum is $$5 + 13 + 18 + 20 + 22 + K + (K + 6) = 84 + 2K$$. So $$84 + 2K = 112$$, which gives $$2K = 28$$ and $$K = 14$$.

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