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Question 1037856: 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 inches high. Two pound weight are 1 1/2 inches high. One pound weights are 1 inch. How much weight can the machine hold?
Answer choices are: 4 pounds, 13 pounds, 20 pounds or 32 pounds.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i would say 32 pounds.
here's why.
the most efficient weight in terms of size is the 5 pounder.
that 5 pounds / 3 inches = 1.67 pounds per inch.
the next most efficient weight in terms of size is the 2 pounder.
that's 2 pounds / 1.5 inches = 1.33 pounds per inch.
the least most efficient weight in terms of size is the 1 pounder.
that's 1 pound / 1 inch = 1 pounds per inch.
to find the maximum weight that the machine can hold, load it up with the most efficient weight and then fill in the rest with the next most efficient rate and on down the scale of efficiency.
20 inches / 3 inches = 6 five pound weights with 2 inches left over.
6 * 5 pounds per weight is equal to 30 pounds.
already you are pointing to the 32 pound capacity since this is clearly in excess of the other capacities shown.
you have 2 inches left over.
you can fill them with the two pound weight and have half an inch left over that can't be filled, or you can fill them with 2 one pound weights and have nothing left over.
either way your total weight is 32 pounds maximum.
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