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South African Mathematics Olympiad

South Africa algebra

Problem

The sums of three out of four numbers (omitting each of the four numbers in turn) are , , and , respectively. What is the sum of the four numbers?
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 .
Final answer
31

Techniques

Simple Equations