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.

ItsTayha
May 10, 2017

#2**+1 **

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

geno3141
May 10, 2017