The Situation
You have five bales of hay.
For some reason, instead of being weighed individually, they were weighed in all possible combinations of two: bales 1 and 2, bales 1 and 3, bales 1 and 4, bales 1 and 5, bales 2 and 3, bales 2 and 4, and so on. The weights of each of these combinations were written down and arranged in numerical order, without keeping track of which weight matched which pair of bales. The weights in kilograms were 80, 82,83, 84, 85, 86, 87, 88, 90, and 91.
Your Task
Your initial task is to find out how much each bale weighs. In particular, you should determine if there is more than one possible set of weights, and explain how you know.
Once you are done looking for solutions, look back over the problem to see if you can find some easier or more efficient way to find the weights.
Write-up
Problem Statement-State the problem in your own words.(5 pts) …show more content…
The bales were weighed in an odd way which you can read about above.
2. Process: This is especially important in this problem. Include a description of any materials you used. Be sure to discuss ways in which you tried to attack the problem but which didn’t lead anywhere. Also discuss any insights you had after working on the problem about other ways you might have solved it. (20 points)
B5+B4 = 91
B5+B3 = 90
So, B4= B3+1
B1+B2 = 80
B1+B3 = 82=> B2= B3-2
So, 82-B3<B5
So, the possible sums are
80, 82, 83, 172-2c, 2c-2, 2c+1, 2c-1, 88, 90, 91
So, 84, 85, 86, 87 are 2B3-1, 2B3+1, 2B3-2, 172-2B3 in some order
So, 2B3-1, 2B3+1 are 85, 87
So, B3 = 43 3. Solution: Show both how you know your weights work and how you know that you have not missed some other possibilities.(10 pts) the five weights are 39, 41, 43, 44,
You have five bales of hay.
For some reason, instead of being weighed individually, they were weighed in all possible combinations of two: bales 1 and 2, bales 1 and 3, bales 1 and 4, bales 1 and 5, bales 2 and 3, bales 2 and 4, and so on. The weights of each of these combinations were written down and arranged in numerical order, without keeping track of which weight matched which pair of bales. The weights in kilograms were 80, 82,83, 84, 85, 86, 87, 88, 90, and 91.
Your Task
Your initial task is to find out how much each bale weighs. In particular, you should determine if there is more than one possible set of weights, and explain how you know.
Once you are done looking for solutions, look back over the problem to see if you can find some easier or more efficient way to find the weights.
Write-up
Problem Statement-State the problem in your own words.(5 pts) …show more content…
The bales were weighed in an odd way which you can read about above.
2. Process: This is especially important in this problem. Include a description of any materials you used. Be sure to discuss ways in which you tried to attack the problem but which didn’t lead anywhere. Also discuss any insights you had after working on the problem about other ways you might have solved it. (20 points)
B5+B4 = 91
B5+B3 = 90
So, B4= B3+1
B1+B2 = 80
B1+B3 = 82=> B2= B3-2
So, 82-B3<B5
So, the possible sums are
80, 82, 83, 172-2c, 2c-2, 2c+1, 2c-1, 88, 90, 91
So, 84, 85, 86, 87 are 2B3-1, 2B3+1, 2B3-2, 172-2B3 in some order
So, 2B3-1, 2B3+1 are 85, 87
So, B3 = 43 3. Solution: Show both how you know your weights work and how you know that you have not missed some other possibilities.(10 pts) the five weights are 39, 41, 43, 44,