February 2019 - Math Problem

You have 4 different weights.  The sum of the weights is 40 grams.  If you have a two pan balance, you can use the 4 weights to make any weight from 1 gram to 40 grams.  How many grams is each of the weights?​

Solution:

​The weights are 1 gram, 3 grams, 9 grams and 27 grams.  

Following this pattern, how many grams would the next weight be?  What range of weights could you make with these 5 weights?

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