Question

Joseph flew home from vacation with a heavy bag. With the first airline he flew, Joseph had to pay $27 to check his bag, plus $24 for every kilogram that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Joseph had to pay $25 per kilogram that his bag was over the weight limit, in addition to the checked bag fee of $16. By coincidence, the fees ended up being the same with both airlines. How far over the weight limit was the bag

Answer 1

To find out how far over the weight limit Joseph's bag was, we need to set up two equations and solve for the weight of the bag.

Step-by-step explanation:

To find out how far over the weight limit Joseph's bag was, we need to set up two equations.

Let's suppose the weight limit for the bag is 'W' kilograms.

With the first airline, Joseph paid $27 to check his bag and $24 for every kilogram over the weight limit. So the cost with the first airline is: Cost_1 = $27 + $24(W - X) where X represents the weight of the bag.

With the second airline, Joseph paid $16 for the checked bag and $25 for every kilogram over the weight limit. So the cost with the second airline is: Cost_2 = $16 + $25(W - X).

Since the fees ended up being the same with both airlines, we can set the two equations equal to each other and solve for X, which represents the weight of the bag:

$27 + $24(W - X) = $16 + $25(W - X)

By simplifying and rearranging the equation, we can find the value of X:

$24(W - X) - $25(W - X) = $16 - $27

$24W - $24X - $25W + $25X = $16 - $27

$-X = -$11

X = 11

Therefore, the bag was 11 kilograms over the weight limit.

Answer 2

Step-by-step explanation:

Flight A :

Checked bag fee = $27

Additional fee per overweight limit = $24

Flight B:

Checked bag fee = $16

Additional fee per overweight limit = $25

Since, the total amount paid for the package on both flights are the same ;

Let x = mass of bag above the weight limit.

Hence, Mathematically ;

27 + 24x = 16 + 25x

24x - 25x = 16 - 27

-x = -11

x = 11

Hence. The bag was s 11kg over the weight limit.