Martha, a caregiver at a wild animal park, is picking up four hippos. She must weigh each of them before she can take them. The only scale large enough to weigh them is a truck scale. The minimum weight that a truck scale can weigh is 300 kg. However, each individual hippo weighs less than 300 kg. She weighs the hippos in every possible pair so that she can figure out the individual weights afterwards. She gets these weights: 312 kg, 356 kg, 378 kg, 444 kg, and 466 kg, but the weight of the sixth pair breaks the scale. What are the weights of the individual hippos? What is the weight of the last pair of hippos who broke the scale?.
There are two possible solutions to the problems. This would not be possible in reality. It would be impossible for there to be more than one weight per hippo, therefore there has to be only one answer to this problem. However, we determined that there are two answers that both work.
In solution one,.
1) Let the weight of one hippo be A, the weight of another hippo be B, and so forth for the weight of each hippo.
Weight of hippos = A, B, C, D.
2) She weighs all possible pairs.
A + B A + C A + D B + C B + D C + D.
3) She gets the following weights:.
312 kg 356 kg 378 kg 444 kg 466 kg 2 heaviest breaks scale.
4) Since the scale minimum is 300 kg, we know that the weight of the heaviest hippo cannot .
exceed 299 kg. We can use the process of trial and error until we have the weights of each hippo. It is possible that one of the hippos could weigh 299 kg; therefore, we assign the weight of hippo A to be 299 kg. Now, we can use the value of A and the weights given in the problem, to solve the rest of the weights. .
466 kg 299 kg = 167 kg, so we know that 299 kg and 167 kg are possible answers because they add up to 466 kg, which is the weight of one of the pairs that is given in the problem.