Question

Jake, Andy, and Damon caught 78 pounds of large mouth bass. Jake caught 22 pounds. Andy caught at least 30 pounds, but no greater than 36 pounds. Which inequality represents the weight (x) of the bass that Damon caught?

Answer 1

The inequality that represents Damon's catch is
20≤x≤26.

Since Jake caught 22 pounds, that means that together, Andy and Damon caught 56 pounds.

The lower limit for Andy is 30 pounds; if he caught this much, then Damon would have caught 56-30=26 pounds.
The upper limit for Andy is 36 pounds; if he caught this much, then Damon would have caught 56-36 = 20 pounds.  This means that Damon's catch is between 20 and 26 pounds.