Atenea has 2 5/6 pounds of trail mix. She makes seven 1/3-pound snack bags with the trail mix for her daily snack for the next week and gives the rest of the trail mix to her brother. How much trail mix does Atenea give to her brother?

First, we need to calculate how much trail mix Atenea uses for her daily snack bags.

7 snack bags x 1/3 pound = 7/3 pounds

Next, we need to subtract the amount used for the snack bags from the total amount of trail mix she has:

2 5/6 pounds - 7/3 pounds = 17/6 pounds - 7/3 pounds
= 17/6 pounds - 14/6 pounds
= 3/6 pounds
= 1/2 pound

Therefore, Atenea gives her brother 1/2 pound of trail mix.