SOLUTION: One month Deandre rented 5 movies and 3 video games for a total of $30. The next month he rented 2 movies and 6 video games for a total of $42. Find the rental cost for each movie

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: One month Deandre rented 5 movies and 3 video games for a total of $30. The next month he rented 2 movies and 6 video games for a total of $42. Find the rental cost for each movie       Log On


   

Question 1153446: One month Deandre rented 5 movies and 3 video games for a total of $30. The next month he rented 2 movies and 6 video games for a total of $42. Find the rental cost for each movie and each video game.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the cost of a movie
Let +y+ = the cost of a video game
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(1) +5x+%2B+3y+=+30+
(2) +2x+%2B+6y+=+42+
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Multiply both sides of (1) by +2+ and
subtract (2) from (1)
(1) +10x+%2B+6y+=+60+
(2) +-2x+-+6y+=+-42+
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+8x+=+18+
+x+=+2.25+
Plug this result back into either equation
(1) +5x+%2B+3y+=+30+
(1) +5%2A2.25+%2B+3y+=+30+
(1) +11.25+%2B+3y+=+30+
(1) +3y+=+18.75+
(1) +y+=+6.25+
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$2.25 = the cost of a movie
$6.25 = the cost of a video game
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check answers:
(1) +5x+%2B+3y+=+30+
(1) +5%2A2.25+%2B+3%2A6.25+=+30+
(1) +11.25+%2B+18.75+=+30+
(1) +30+=+30+
OK
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