Question

One month Pablo rented 12 movies and 2 video games for a total of $65. The next month he rented 3 movies and 5 video games for a total of $41. Find the rental cost for each movie and each video game.

Answer 1

The rent for one movie is $4.50 and rent for one video game is $5.50

Step-by-step explanation:

Let,

Rent for one movie = x

Rent for one video game = y

According to given statement;

12x+2y=65     Eqn 1

3x+5y=41        Eqn 2

Multiplying Eqn 2 by 4

$4(3x+5y=41)\\12x+20y=164\ \ \ \ Eqn\ 3$

Subtracting Eqn 1 from Eqn 3

$(12x+20y)-(12x+2y)=164-65\\12x+20y-12x-2y=99\\18y=99$

Dividing both sides by 18

$\frac{18y}{18}=\frac{99}{18}\\y=5.50$

Putting y=5.50 in Eqn 2

$3x+5(5.50)=41\\3x+27.50=41\\3x=41-27.50\\3x=13.50$

Dividing both sides by 3

$\frac{3x}{3}=\frac{13.50}{3}\\x=4.50$

The rent for one movie is $4.50 and rent for one video game is $5.50

Keywords: linear equation, elimination method

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