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25 September, 05:52

On a plane, two men together had 135 kilograms of luggage. The first paid $1.35 for his excess luggage and the second paid $2.70 for his excess luggage. Had all the luggage belonged to one person, the excess luggage charge would have been $8.10. At most how many kilograms of luggage is each person permitted to bring on the plane free of additional charge?

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  1. 25 September, 06:09
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    45kg.

    Step-by-step explanation:

    Let X be the # of kilograms allowed without a charge.

    Let Y be the # of kilograms of luggage carried by person A.

    Let Z be the # of kilograms of luggage carried by person B.

    Let P be the price / kilogram of excess baggage.

    We need to solve for X.

    We know the following is true:

    Y + Z = 135

    (Y - X) * P = 1.35

    (Z - X) * P = 2.70

    (135 - X) * P = 8.10

    Now, it's just the messy problem of solving 4 equations for 4 unknowns. The answer turns out to be:

    P = 0.09

    Z = 75

    Y = 60

    X = 45

    Therefore, at most, each person is allowed 45 kilograms of luggage at no additional charge.
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