Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142. I need help with this problem, and I was thinking in this way:
$$ x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} + x_{7} = 332 $$
and I need to find three of these which sum is at least 142.
But I don't know what next. 
Any help would be appreciated

Assume $x_1\le x_2\le\ldots\le x_7$.  Here's a proof that $x_5+x_6+x_7\ge144$ (which answers an observation made by TonyK in comments).  
Suppose $x_5+x_6+x_7\le143$.  Then $x_1+x_2+x_3+x_4\ge332-143=189$, which implies $x_4\ge189/4=47.25$.  Since the ages are assumed to be integers, we have $48\le x_4\le x_5\le x_6\le x_7$, which contradicts the supposition.
