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 .

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 .