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One month rita rented 5 movies and 2 video games for a total of $26 . The next month she rented 3 movies and 8 video games for a total of $53 . Find the rental cost for each movie and each video game.

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sqdancefan

Given

  • 5 movies and 2 video games rent for $26
  • 3 movies and 8 video games rent for $53

Find

  • the rental cost of each

Solution

Let m and v represent the rental cost of a movie and a video game, respectively. The given information can be expressed in two equations:

... 5m +2v = 26

... 3m +8v = 53

Using Cramer's rule, we can find the solution to be

... m = (2·53 -8·26)/(2·3-8·5) = -102/-34 = 3

... v = (26·3-53·5)/-34 = 5.50

The rental cost for each movie is $3; for each video game is $5.50.

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The Vedic math variation of Cramer's Rule tells you the solution to

  • ax+by=c
  • dx+ey=f

is ...

  • x=(bf-ec)/(bd-ea)
  • y=(cd-fa)/(bd-ea)