Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.5 Junior Find the answer

What is the value of $x$ if the three numbers $2, x$ , and 10 have an average of $x$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since the average of $2, x$ and 10 is $x$ , then $\frac{2 + x + 10}{3} = x$ . Multiplying by 3, we obtain $2 + x + 10 = 3x$ . Re-arranging, we obtain $x + 12 = 3x$ and then $2x = 12$ which gives $x = 6$ .

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