Kangaroo Airlines charges an additional fee for overweight baggage. The fee for each kilogram of additional baggage past a certain weight limit per passenger is the same. The baggage which Mr. and Mrs. Sierowski brought together weighed 60 kilograms, and they paid $3 in overweight baggage fees. Mr. Miklovich's baggage also weighed 60 kilograms, but he paid $10.50 in overweight baggage fees. What is the maximum baggage weight in kilograms allowed per passenger on Kangaroo Airlines? We have a lot of variables in place, so let's name the total weight per passenger as W. That would be max kilograms per passenger and baggage. And then we have Mr. M's baggage, which is 60 kilograms, and we have C1 plus C2, the two sets of baggage brought by Mr. and Mrs. Sierowski, and that's together 60 kilograms. And we also have this fee F, which is the fee per kilogram of overweight. And so we know that $10.50 is the fee that Mr. M paid, which is the difference between the maximum allowed weight and 60 kilograms, multiplied by this fee F. Now we know that $3 is the fee paid by Mr. and Mrs. C, and both of them had an overweight, so we have two of these equations, and we know that there are two exactly, because if we assume that, let's say Mr. C didn't have an overweight baggage, this part of the equation, this term would be gone, and then we would have one set of overweight luggage, which would have to incur the same fee as Mr. M's luggage. So we know we have two additional overweight sets of luggage, one for Mr. and one for Mrs. C, and then we can solve this equation by substitution. We can solve for F and substitute that into here and here, and remember that C1 plus C2 is 60, and then finally solve the equation. So what we have is, after substituting 3, I'll factor out the F here, is W, 2W actually, minus the sum C1 plus C2. And so continuing on up here, that gives us that 3 is equal to F, we can solve for, that's 10.5 divided by W minus 60, and that's multiplied by 2W minus C1 plus C2 is equal to 60 again. So here is a little trick we can do to make our calculation slightly simpler. I'll expand this as W plus W minus 60, so it will be slightly easier to compute. And then multiplying out, we have 3 is equal to 10.5W divided by W minus 60 plus, now there is some cancellation here, and we have just plus 10.5. So this gives us that, after subtracting 10.5, negative 7.5 is equal to 10.5W over W minus 60, and we can multiply by W minus 60 on both sides, and by a minus 1 at the same time. So we have 60 minus W times positive 7.5 is equal to 10.5W, and that gives us 7.5 times 60 minus 7.5W is equal to 10.5W, or finally that 7.5 times 60 is equal to 18W. We can multiply both sides by 10, for example, to obtain that W is 75 times 60 divided by 180, which gives us 75 divided by 3, and that's finally equal to 25 in kilograms. So that is the weight limit after solving this equation, which gives us the answer D.

Kangaroo Airlines

baggage weight

overweight fee

equations

weight limit