You are purchasing an exercise machine for a physical therapy office. the machine has a 20 inch vertical space where you add weights to increase the resistance for the patient. five pound weights are 3" high. two pound weights are 1 ½" high. one pound weights are 1". how much weight can the machine hold?

The maximum weight that could be held would be 32 pounds. or six five pound weights taking up 18 inches of space, and weighing 30 Lbs, and two one pound weights adding another two inches. You could achieve a greater weight if you had a weight of one-half inch, in which case you could take six 5 lb weights and 1 two  pound weight, then you could add a half inch weight bringing the weight to over 32 inches. Since we don't have a half inch weight we can't raise the weight above 32lbs.