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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Gavin flew home from vacation with a heavy bag. With the first airline he flew, Gavin had to pay to check his bag, plus for every kilogram that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Gavin had to pay per kilogram that his bag was over the weight limit, in addition to the checked bag fee of . 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?The bag was ___ kilograms over the weight limit, and each airline's fee was ___.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Gavin flew home from vacation with a heavy bag. With the first airline he flew, Gavin had to pay to check his bag, plus for every kilogram that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Gavin had to pay per kilogram that his bag was over the weight limit, in addition to the checked bag fee of . 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?The bag was ___ kilograms over the weight limit, and each airline's fee was ___.
- Formulate Equations: Let's denote the weight over the limit as kilograms and the fee charged by each airline as dollars.The first airline's fee can be represented by the equation:The second airline's fee can be represented by the equation:Since the fees ended up being the same, we can set these two equations equal to each other to form a system of equations.
- Write System of Equations: Write the system of equations based on the information given:Since is the same for both equations, we can set the right sides of the equations equal to each other:
- Solve for x: Solve for x by subtracting from both sides of the equation:
- Calculate Bag Weight: Subtract from both sides to solve for : This means Gavin's bag was kilograms over the weight limit.
- Find Airline Fees: Now, we can find the fee charged by each airline by substituting back into either of the original equations. Let's use the first airline's equation:So, each airline's fee was .
