+108 Tim flew home from holiday with a heavy bag. With the first airline he flew, Tim had to pay $20 to check his bag, plus $22 for every kilogram that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Tim had to pay $19 per kilogram that his bag was over the weight limit, in addition to the checked bag fee of $32. 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?
Each airline's fee was $, and the bag was kilograms over the weight limit.
+23252 Let k represent the number of kilograms over the weight limit.
First airline: Fee = $20 + $22k
Second airline: Fee = $32 + $19k
Since the fees were equal: $20 + $22k = $32 + $19k
Subtracting $19k from both sides: $20 + $3k = $32
Subtracing $20 from both sides: $3k = $12
Dividing by 4: k = 4 <-- the bag was 4 k overweight.
First airline: Fee = $20 + $22k ---> Fee = $20 + $22(4) = $20 + $88 = $108
Second airline: Fee = $32 + $19k ---> Fee = $32 + $19(4) = $32 + $76 = $108
