Question

Emir flew home from vacation with a heavy bag. With the first airline he flew, Emir had to pay $20 to check his bag, plus $10 for every pound that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Emir had to pay $5 per pound that his bag was over the weight limit, in addition to the checked bag fee of $30. By coincidence, the fees ended up being the same with both airlines. How large was each airline's fee?

Answer 1

$27.5

Explanation:

Let

x = pound over weight limit

Airline 1 = 20 + 10x

Airline 2 = 5 + 30x

Equate the fees

20 + 10x = 5 + 30x

20 - 5 = 30x - 10x

15 = 20x

x = 15/20

x = 0.75 pounds

How large was each airline's fee?

Airline 1 = 20 + 10x

= 20 + 10(0.75)

= 20 + 7.5

= $27.5

Airline 2 = 5 + 30x

= 5 + 30(0.75)

= 5 + 22.5

= $27.5