Question

One month Yoko rented 3 movies and 5 video games for a total of $40. The next month she rented 9 movies and 7 video games for a total of $74. Find the rental cost for each movie and each video game.

Answer 1

Answer:

• movie: $3.75
• video game: $5.75

Step-by-step explanation:

Two equations in two unknowns can be written:

  3m +5v = 40

  9m +7v = 74

These can be solved a variety of ways. One of them is using Cramer's rule. It tells you the solution to

• ax +by = c
• dx +ey = f

is given by ...

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

For the numbers above,

• ∆ = 5·9 -7·3 = 24
• m = (5·74 -7·40)/24 = 90/24 = 3.75
• v = (40·9 -74·3)/24 = 138/24 = 5.75

The rental cost for each movie is $3.75; for each video game, it is $5.75.

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The attached graph shows a graphing calculator solution to these equations.