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?

Question

Mathematics

Park

25 January, 18:19

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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Answers (1)

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Alana Pacheco · Answer 1

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.