Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 3.9 AMC 10/12 Find the answer South Africa

If the average of four different positive integers is $8$ , what is the largest possible value of any one of these integers?

Your answer

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

Solution

If the average of four numbers is $8$ , their sum must be $8 \times 4 = 32$ . To maximize the largest one of these numbers, we choose the smallest possible values for the other three, which are $1$ , $2$ and $3$ (since the integers must be positive and different). The remaining number is then $32 - (1 + 2 + 3) = 26$ .

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