Question

One month Ivan rented 8 movies and 3 video games for a total of $43. The next month he rented 2 movies and 5 video games for a total of $32. Find the rental cost for each movie and each video game.

Answer 1

Given

Let's represent movies with M

Let's represent video with V

`\begin{gathered} 8m+3v=43\ldots\text{Equation 1} \\ 2m+5v=32\ldots\text{Equation 2} \end{gathered}`

Solution

Using substitution method

I will solve your system by substitution.

`\begin{gathered} 8m+3v=43\ldots\text{Equation 1} \\ \text{Make M the subject of the formula} \\ 8m=43-3v \\ \text{Divide both sides by 8} \\ m=(43-3v)/(8)\ldots\text{Equation 3} \end{gathered}`

Substitute for m in Equation 2

`\begin{gathered} 2((43-3v)/(8))+5v=32 \\ \\ (43-3v)/(4)+5v=32 \\ \end{gathered}`

To clear the fraction multiply all through by 4

`\begin{gathered} (43-3v)/(4)*4+5v*4=32*4 \\ \\ \\ 43-3v+20v=128 \end{gathered}`

Separate the similar term

`\begin{gathered} -3v+20v=128-43 \\ 17v=85 \\ \text{Divide both sides by 17} \\ (17v)/(17)=(85)/(17) \\ \\ v=5 \end{gathered}`

Substitute for v =5 in equation 3

`\begin{gathered} m=(43-3v)/(8)\ldots\text{Equation 3} \\ m=(43-3(5))/(8) \\ m=(43-15)/(8) \\ \\ m=(28)/(8) \\ \\ m=(7)/(2)=3.5 \end{gathered}`

The rental cost for each movie

`m=\text{ \$}3.50`

The rental cost for each video game.

`v=\text{ \$5}`