A Gold Diggers Mind Essay

Submitted By bob-griffin

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A Gold Diggers Mind
Problem Statement There were 5 different gold nuggets that were found in the mountains by a gold digger. A combination of two nuggets weight were added together, each combination being different, to get a weight of 40, 42, 43, 44, 45, 46, 47, 48, 50, or 51. Find the weight of each individual nugget.
Process
First, we decided each nuggets weight would be close to 20-25, narrowing down the choices. Then, we created a table to test different weights of the individual nuggets to see which are close and which need to be altered. To get a starting point, we said nuggets 1 and 2 weighed 19 and 21, to get a total weight of 40. Then we said another nugget weighed 23, so that 23 and 21 could be added to equal 43. This continued until we ran into a problem and couldn’t add 2 nuggets together to get one of the total weights. When this happened, we went back and revised what we have previously said to be the answer. Then we did the whole process all over, continuing to do this until we got the answer. Our group took the trial and error approach, and it worked fine.
Solution
The individual weights of the nuggets are 19, 21, 23, 24, and 27. You can tell these are the answer because if you take any of the 2 nuggets and combine them, they make one of the 10 possible weights. To test this, set up multiple math problems with the weight of the nuggets: 19+21, 19+23, 19+24, 19+27, 21+23, and so on. The final sum, if continued to set up problems following the pattern I’ve started, will be 40, 42, 43, 44, 45, 46, 47, 48, 50 and 51. These all match the original 10 weights we were given at the start of the problem. Thus, the answer to the problem is that the weights of each nugget are , 21, 23, 24, and 27.
Extensions
1. Are there

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