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Solving A System of Equations

Solving A System of Equations. Airam Salinas & Fatima Gonzalez December 18, 2013 7-8 A. Problem Situation. A cruise ship has 680 rooms. Those with a view rent for $160 per night and those without a view rent for $105 per night.

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Solving A System of Equations

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  1. Solving A System of Equations Airam Salinas & Fatima Gonzalez December 18, 2013 7-8 A

  2. Problem Situation • A cruise ship has 680 rooms. • Those with a view rent for $160 per night and those without a view rent for $105 per night. • On a night when the ship was completely occupied, revenues were $92,500. • How many of each type of room are on the ship?

  3. Define Variables • The variables in these equation are Awhich represents the number of rooms with a view, which costs $160 per night, and F which represents the number of rooms without a view, which costs $105 per night.

  4. System of Equations • Our system of equations are • 92,500 = 160A + 105F • A + F = 680

  5. Solution method To solve this equation you will have to use substitution. • First you need to rewrite one of the equations: • A + F = 680 • Solve for F: • F = 680 - A • Now substitute into the other equation. • 92500 = 160A + 105(680-A) • 92500 = 160A + 71400 - 105A • 92500 = 55A + 71400 • -71400 -71400 • 21100 = 55A • 21100/55 = A A=383.64 F=296.36

  6. Solution to the System of Equations • (A, F) • (383.64, 296.36)

  7. Check of Solution • 92,500 = 160(383.64) + 105(296.36) True • 383.64 + 296.36 = 680 True

  8. Solution in the Problem Situation • The number of rooms has to be a whole number in order to make sense in this problem situation. • 383.64 is the number of rooms with a view. • 296.36 is the number of rooms without a view.

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