A shipping clerk has five boxes of different but unknown weights each weighing less than 100 kg. The clerk weights the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?
The answer options are given as 60,65,64,62. 62 is given as the correct answer in the book and it is written that the other boxes shall then weigh 59,54,58,56.
I want to know the method used for arriving at the answer in these type of questions.
[Math] weight of heaviest box
elementary-number-theory
Best Answer
Hint:
None of the weights can be the same or there would be repeated results Define the weights $a<b<c<d<e$
You know the smallest two boxes and the largest two boxes result in the smallest and largest weights. So:
$$110=a+b$$ $$121=d+e$$
As the next smallest and largest must coehcide with third lightest and heaviest respectively.
$$112 = a+c$$ $$120 = e+c$$
Finally if you add up all combinations:
$$1156 = 4a+4b+4c+4d+4e$$
This is 5 equations to solve 5 variables. I think you should be able to do this.