Question

please answer as soon as possible​

Answer 1

Answer:

25 kg

Step-by-step explanation:

Let m be the free luggage allowance for each passenger.

Let a be the amount (in kg) that the first passenger's luggage exceeds m, and b be the amount that the second passender's luggage exceeds m.

So the passengers have m+a and m+b kilograms of luggage each.

The basic idea now is to use the given information to get some equations involving m, a and b.  Then we eliminate a and b to get the value of m, which is what we need.

The total of the luggage is 2m + a + b = 100.       ... (1)

If one person carried all the 100kg of luggage, this would exceed m by 100-m.

So the cost per kilogram for excess luggage is:

(100-m)/30 = a/12 = b/8.

Therefore  a/12 = b/8  =>  2a = 3b   ... (2)

and  (100-m)/30 = a/12  =>  2(100-m) = 5a   =>   2m + 5a = 200.   ... (3)

Multiplying equation (1) by 3 gives 6m + 3a + 3b = 300, and substituting equation (2), this becomes

6m + 3a + 2a = 300  =>  6m + 5a = 300.   ... (4)

Subtracting equation (3) from equation (4) now gives

4m = 100  =>  m = 25.

Hence the free luggage allowance for each passenger is 25 kg.