Question

One month Ravi rented4 movies and8video games for a total of $57 The next month he rented2 movies and3 video games for a total of$ 23 Find the rental cost for each movie and each video game. One month Ravi rented4 movies and8 video games for a total of$ 57 The next month he rented2 movies and 3 video games for a total of$23 Find the rental cost for each movie and each video game. Rental cost for each movies $??Rental cost for each vidéo games $ ??

Answer 1

Given the question in the question tab, the following are the solution steps to get the rental cost for each movie and each video game.

Step 1: Write the representation for the two rentals

Let m represents movies

Let v represent video games

Step 2: Write the statements in form of a mathematical equation

`\begin{gathered} \text{Month 1: }4m+8v=57 \\ \text{Month 2: }2m+3v=23 \end{gathered}`

Step 3: Solve the equations above simultaneously using elimination method to get the values of m and v

`\begin{gathered} 4m+8v=57----(1) \\ 2m+3v=23----(2) \\ \text{ multiply equation 1 by 2 and equation 2 by }4 \\ 8m+16v=114----(3) \\ 8m+12v=92----(4) \\ \text{subtract equation (4) from equation (3)} \\ 4v=22 \\ v=(22)/(4)=5.5 \\ \text{Substitute 5.5 for v in equation 1 to get the value of m} \\ 4m+8v=57 \\ 4m+8(5.5)=57 \\ 4m+44=57 \\ 4m=57-44=13 \\ m=(13)/(4)=3.25 \\ m=\text{\$}3.25,v=\text{\$}5.50 \end{gathered}`

Rental cost for each movies is $3.25

Rental cost for each video games $5.50