Molly flew home from vacation with a heavy bag. With the first airline she flew, Molly had to pay $20 to check her bag, plus $26 for every kilogram that her bag was over the weight limit. The next flight was with another airline that had the same weight limit. Molly had to pay $20 per kilogram that her bag was over the weight limit, in addition to the checked bag fee of $26. By coincidence, the fees ended up being the same with both airlines. How large was each airline's fee? How far over the weight limit was the bag?
Question
Molly flew home from vacation with a heavy bag. With the first airline she flew, Molly had to pay 26 for every kilogram that her bag was over the weight limit. The next flight was with another airline that had the same weight limit. Molly had to pay 26. By coincidence, the fees ended up being the same with both airlines. How large was each airline's fee? How far over the weight limit was the bag?
Solution
The problem can be solved by setting up two equations based on the information given and then solving for the unknowns.
Let's denote:
- F as the total fee Molly had to pay for each airline
- W as the weight by which Molly's bag exceeded the weight limit
From the problem, we know that:
-
With the first airline, Molly had to pay a 26 for every kilogram over the weight limit. This can be written as: F = 20 + 26W
-
With the second airline, Molly had to pay a 20 for every kilogram over the weight limit. This can be written as: F = 26 + 20W
Since the fees ended up being the same with both airlines, we can set the two equations equal to each other and solve for W:
20 + 26W = 26 + 20W 26W - 20W = 26 - 20 6W = 6 W = 1
Substituting W = 1 into either of the original equations will give us the total fee F:
F = 20 + 26*1 = $46
So, each airline's fee was $46 and the bag was 1 kilogram over the weight limit.
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