Question

1 months amren 5 movies and 3 video games for a total of $36. the next month he went 7 movies and 9 video games for a total of $78. find the rental cost for each movie in each video game.rental cost for each movie:rental cost for each video games:

Answer 1

Each movie cost $3.75 while each video game cost $5.75

Here, we want to get rental costs

We start by using variables to represent the costs of the movie and the video game

Let the cost of a movie be m and the cost of a video game be g

Thus, we have it that;

`5m\text{ + 3g = 36}`

and;

`7m\text{ + 9g = 78}`

So, we have two equations to solve simlutaneously

That would yield;

`\begin{gathered} \text{From i;} \\ 5m\text{ + 3g = 36} \\ 3g\text{ = 36-5m} \\ we\text{ can have equation }ii\text{ as;} \\ 7m\text{ + 3(3g) = 78} \\ 7m\text{ + 3(36-5m) = 78} \\ 7m\text{ + 108-15m = 78} \\ 108-78\text{ = 15m-7m} \\ 8m\text{ = 30} \\ m\text{ = }(30)/(8) \\ m\text{ = \$3.75} \end{gathered}`

Now, to get the value of g, we make a substitution into any of the equations;

`\begin{gathered} 3g\text{ = 36-5m} \\ 3g\text{ = 36-5(3.75)} \\ 3g\text{ = 36-18.75} \\ 3g\text{ = 17.25} \\ g\text{ = }(17.25)/(3) \\ g\text{ = 5.75} \end{gathered}`