Question

one month Lisa rented 3 movies and 5 video games for a total of $43. The next month she rented 9 movies and 7 video games for a total of $83. Find the rental cost of each movie and video game.

Answer 1

The rental cost of each movie and video game is $4.75 & $5.75 respectively .

Step-by-step explanation:

Here we have the following info: one month Lisa rented 3 movies and 5 video games for a total of $43. The next month she rented 9 movies and 7 video games for a total of $83. Let's form up linear equations for the following scenarios:

one month Lisa rented 3 movies and 5 video games for a total of $43:

Let rental cost of each movie and video game is $x & $y respectively . then

⇒ $3x+5y=43$  ... (1)

The next month she rented 9 movies and 7 video games for a total of $83:

⇒ $9x+7y=83$ ..... (2)

Let's solve equation (1) & (2) ..

Multiply (1) by 3 and subtract (1) , (2):

⇒ $3(3x+5y)- (9x+7y) = 3(43) - 83$

⇒ $15y-7y = 46$

⇒ $8y = 46$

⇒  $y = 5.75$

Putting value in equation (1):

⇒ $3x+5y= 43$

⇒ $3x+5(5.75)= 43$

⇒ $x = 4.75$

∴ The rental cost of each movie and video game is $4.75 & $5.75 respectively .