Question

write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
erin flew home from vacation with a heavy bag. with the first airline she flew, erin had to pay $16 to check her bag, plus $10 for every kilogram that her bag was over the weight limit. the next flight was with another airline that had the same weight limit. erin had to pay $9 per kilogram that her bag was over the weight limit, in addition to the checked bag fee of $22. by coincidence, the fees ended up being the same with both airlines. how large was each airlines fee? how far over the weight limit was the bag?
each airlines fee was $ , and the bag was kilograms over the weight limit.

Explanation:

Step1: Set up equations

Let \(x\) be the number of kilograms over the weight limit.
For the first airline, the fee \(y = 16+10x\).
For the second airline, the fee \(y=22 + 9x\).

Step2: Substitute \(y\)

Since \(y\) is the same for both airlines, we substitute \(y\) in the equations:
\(16+10x=22 + 9x\).

Step3: Solve for \(x\)

Subtract \(9x\) from both sides: \(16+10x-9x=22 + 9x-9x\), which gives \(16+x=22\).
Subtract \(16\) from both sides: \(x=22 - 16\), so \(x = 6\).

Step4: Solve for \(y\)

Substitute \(x = 6\) into the first - airline's fee equation \(y=16+10x\).
\(y=16+10\times6=16 + 60=76\).

Answer:

Each airline's fee was \(\$76\), and the bag was \(6\) kilograms over the weight limit.