Question

Eli flew home from vacation with a heavy bag. With the first airline he flew, Eli had to pay $29 to check his bag, plus $18 for every kilogram that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Eli had to pay $19 per kilogram that his bag was over the weight limit, in addition to the checked bag fee of $18. By coincidence, the fees ended up being the same with both airlines. solve answer without using C_2

Answer 1

To solve the problem, we need to set up equations based on the fees charged by both airlines.

Let's denote:

• \( w \): the weight of Eli's bag (in kilograms)
• \( l \): the weight limit (in kilograms)
• \( x \): the amount by which the bag is over the weight limit (i.e., \( x = w - l \))

The fees for the two airlines can be expressed as follows:

1. First Airline:

   • Checked bag fee = $29
   • Additional fee for being over weight = $18 per kilogram over the limit
   • Total fee: \[ \text{Fee}_1 = 29 + 18x \]

2. Second Airline:

   • Checked bag fee = $18
   • Additional fee for being over weight = $19 per kilogram over the limit
   • Total fee: \[ \text{Fee}_2 = 18 + 19x \]

According to the problem, the fees from both airlines are the same, so we can set the two equations equal to each other: \[ 29 + 18x = 18 + 19x \]

Now, let's solve for \( x \).

1. Subtract \( 18x \) from both sides: \[ 29 = 18 + x \]

2. Subtract 18 from both sides: \[ 29 - 18 = x \] \[ x = 11 \]

Now we know that Eli's bag is 11 kilograms over the weight limit. To find the weight of Eli's bag, we can express it in terms of the weight limit: \[ w = l + x = l + 11 \]

Next, we can substitute \( x = 11 \) into either fee equation to find the total fee. Let's use the equation for the first airline: \[ \text{Fee}_1 = 29 + 18(11) = 29 + 198 = 227 \]

So regardless of the weight limit, both airlines charged Eli \( $227 \) for checking his bag.

In summary:

• The amount Eli's bag was over the weight limit: 11 kilograms
• The total fee paid by Eli: $227