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
Suppose that any $3$ chosen people have at most a total age of $141$. Then, $x_1 + x_2 + x_3 \le 141$ and so is $x_4 + x_5 + x_6$. This indicates that $x_7 \ge 50$. 

Repeating the same process exchanging the roles of $x_i$'s yields $x_i \ge 50$ for any $i$. Which leads to a contradiction.
The average integer age of all $7$ is $47$. $3 \times 47 = 141$. However, because $7 \times 47 = 329$, it follows that one person must have an age of $50$ in order for the total to be $332$. Take $2$ average people and the old guy and you have $144$.