Question

Chase is an experienced whitewater rafter who guides groups of adults and children out on the water for amazing adventures. The raft he uses can hold 800 pounds of weight. Any weight greater than 800 pounds can cause the raft to sink, hit more rocks, and/or maneuver more slowly.

Chase estimates the weight of each adult as approximately 200 pounds and the weight of each child as approximately 100 pounds. Chase charges adults $75 and children $50 to ride down the river with him. His goal is to earn at least $150 each rafting trip.

Assume a represents the adult rafters, and c represents the number of children. Which inequality represents valid constraints for the situation above?

Hint: When factoring the cost of adults, the guide will not charge himself, so you should subtract 1 from the number of adults paying.

Answer 1

Let a = total adults (including Chase) and c = number of children.

Weight constraint:
200a + 100c ≤ 800

Revenue constraint (Chase doesn't pay):
75(a − 1) + 50c ≥ 150

You can simplify these:
4a + 2c ≤ 16 and 3a + 2c ≥ 9

Also a ≥ 1, c ≥ 0 (and a, c integer).