An airline charges 380 dollar for a round-trip flight from...

An airline charges 380 dollar for a round-trip flight from New York to Los Angeles if the ticket is purchased at least 7 days in advance of travel. Otherwise, the price is 700 dollar . If a total of 80 tickets are purchased at a total cost of 39,040 dollar, find the number of tickets sold at each price.

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Key Concepts

System of Linear Equations

This involves setting up two or more linear equations that simultaneously describe the different conditions in a problem. In cases where there are multiple unknowns, each equation represents a different constraint, and solving the system yields the values of these unknowns.

Elimination and Substitution Methods

These are standard techniques used to solve systems of linear equations. The substitution method involves expressing one variable in terms of another and substituting that expression into another equation, while the elimination method consists of adding or subtracting equations to remove one of the variables so that the remaining variable can be solved directly.

Word Problem Translation

This concept involves interpreting a verbal description of a scenario into mathematical expressions such as equations. It requires identifying unknown quantities and relationships between them, and then accurately representing the conditions provided in the problem with algebraic equations.

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