Question

Sasha flew home from vacation with a heavy bag. With the first airline she flew, Sasha had to pay $21 to check her bag, plus $12 for every pound that her bag was over the weight limit. The next flight was with another airline that had the same weight limit. Sasha had to pay $7 per pound that her bag was over the weight limit, in addition to the checked bag fee of $31. By coincidence, the fees ended up being the same with both airlines. How far over the weight limit was the bag? How large was each airline's fee?

Answer 1

Answer:

Sasha bag was 2 pounds over the limit.

Total Cost for each Airline was $45.

Step-by-step explanation:

Let the number of pound over the weight limit be 'x'.

For Airline 1:

Given;

Amount for checking the bag = $21

Amount for each extra pound over the limit = $12

So we can say that;

Total amount paid in Airline 1 is equal to Sum of Amount for checking the bag and Amount for each extra pound over the limit multiplied by number of pound over the weight limit.

framing in equation form we get;

Total amount paid in Airline 1 = $21+12x$

For Airline 2:

Given;

Amount for checking the bag = $31

Amount for each extra pound over the limit = $7

So we can say that;

Total amount paid in Airline 2 is equal to Sum of Amount for checking the bag and Amount for each extra pound over the limit multiplied by number of over pound weight limit.

framing in equation form we get;

Total amount paid in Airline 2 = $31+7x$

We need to find how far over the weight limit was the bag.

Also we need to find how large was each airline's fee.

Now Given that;

the fees ended up being the same with both airlines.

So we can say that;

Total amount paid in Airline 1 = Total amount paid in Airline 2

$21+12x=31+7x$

Combining the like terms we get;

$12x-7x=31-21\\\\5x =10$

Dividing both side by 5 we get;

$\frac{5x}{5}=\frac{10}{5}\\\\x=2\ pounds$

Hence Sasha bag was 2 pounds over the limit.

Total amount paid in Airline 1 = $21+12x=21+12\times2 = 21+24 =\ 45$

Total amount paid in Airline 2 = $31+7x=31+7\times2 = 31+14 =\ 45$

Hence Total Cost for each Airline was $45.