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Find the sum of the ages of 4 the men

This is the complete problem:
There are 4 men in a car. Find the sum of the ages of 4 the men if their ages in all possible pairs are given as : 96, 79, 84, 95, 100, 83.

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Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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a + b
a + c
a + d
b + c
b + d
c + d
------
3(a + b + c + d)
 
96 = 90 + 6
79 = 90 - 11
84 = 90 - 6
95 = 90 + 5
100=90 + 10
83 = 90 - 7
       ----------
     6(90) - 3 = 3(a + b + c + d)
 
(a + b + c + d) = 2(90) - 1 = 179