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

The sums of three out of four numbers (omitting each of the four numbers in turn) are 2020, 2222, 2424 and 2727, respectively. What is the sum of the four numbers?

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

Solution

Since each of the given sums involves exactly three of the numbers, it follows that the sum of the four sums is three times the sum of the four numbers. Thus the required sum is equal to (20+22+24+27)/3=93/3=31(20 + 22 + 24 + 27)/3 = 93/3 = 31.

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