2500.71 – Airplane Baggage

Declan Bogtrotter and his wife Sharon took an airplane to Rome, on the small airline Air Barataria. They had together 94 pounds of baggage. He paid $25 and she paid $17 for the excess weight. If Declan had made the trip by himself with the combined baggage of both of them, he would have had to pay $162. How many pounds of baggage can one person take along without charge?

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Solution

Let ff = free pounds per person. Together they took 94 pounds of baggage.

Let rr = rate per pound overweight.

(94–2f)r=42 together(94 – 2f)r = 42 \text{ together}

(94–f)r=162 alone(94 – f)r = 162 \text{ alone}

94r−2fr=4294r−fr=16294r=282\begin{aligned}94r - 2fr &= 42 \\94r - fr &= 162 \\94 r &= 282\end{aligned}

r=28294r = \dfrac{282}{94} = $3 per pound

fr=$120fr = \$120 so ff = 40 pounds.