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