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?
Solution
Let f = free pounds per person. Together they took 94 pounds of baggage.
Let r = rate per pound overweight.
(94 – 2f)r = 42 together
(94 – f)r = 162 alone
94r – 2fr = 42
94r – fr = 162
94 r = 282
r = 282/94 = $3 per pound
fr = $120 so f = 40 pounds.