# 1955 AHSME Problems/Problem 38

## Problem 38

Four positive integers are given. Select any three of these integers, find their arithmetic average, and add this result to the fourth integer. Thus the numbers , and are obtained. One of the original integers is:

## Solution

Define numbers and to be the four numbers. In order to satisfy the following conditions, the system of equation should be constructed. (It doesn't matter which variable is which.) Adding all of the equations together, we get: . This means that .

We can determine that . This, with some algebra, means that . must be .

## See Also

In order to see the rest of the problem set, click here

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