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A mini truck with a livestock carrying permit is allowed to carry animals at a time whose total weight should not be more than 1000 kg. What is the maximum number of animals that can be loaded in the truck if there is exactly one animal weighing 103 kg (which must be loaded on the truck), exactly one animal weighing 93 kg, and the weight of all other animals is between 93 kg and 103 kg?

Answer :

To solve this problem, we need to determine the maximum number of animals that can be loaded in the truck without exceeding the total weight limit of 1000 kg.

Step-by-Step Solution

  1. Determine the required load that must be included:

    • There are two specific animals we must definitely load on the truck. The first weighs 103 kg and the second weighs 93 kg.

  2. Calculate the combined weight of these two animals:

    [tex]\text{Total weight of required animals} = 103 \, \text{kg} + 93 \, \text{kg} = 196 \, \text{kg}[/tex]

  3. Find the remaining weight capacity of the truck:

    [tex]\text{Remaining weight capacity} = 1000 \, \text{kg} - 196 \, \text{kg} = 804 \, \text{kg}[/tex]

  4. Consider the weights of the other animals:

    • We know that all other animals weigh between 93 kg and 103 kg. To maximize the number of additional animals, we should use the smallest possible weight for these animals, which is 93 kg.

  5. Calculate the maximum number of additional 93 kg animals we can load:

    [tex]\text{Number of additional animals} = \left\lfloor \frac{804 \, \text{kg}}{93 \, \text{kg/animal}} \right\rfloor = \left\lfloor 8.645 \right\rfloor = 8[/tex]

    (Here, [tex]\lfloor x \rfloor[/tex] denotes the greatest integer less than or equal to [tex]x[/tex]).

  6. Calculate the total number of animals that can be loaded on the truck:

    • The maximum number of animals that can be loaded in the truck is the sum of the 2 required animals plus the 8 additional animals:

    [tex]\text{Total number of animals} = 2 + 8 = 10[/tex]

Therefore, the maximum number of animals that can be loaded in the truck is 10, given the constraints specified.

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Rewritten by : Barada