System of linear equations

Question

1 month San rented 8 movies in three video games for a total of $51 the next month he rented rented two movies in 5 video games for a total of $34 find the rental cost for each movie and each video game

Answer 1

1 month San rented 8 movies in three video games for a total of $51 the next month he rented rented two movies in 5 video games for a total of $34 find the rental cost for each movie and each video game

Given:

8 movies and 3 video games total 51

2 movies and 5 video games total 34

Find:

Cost for each movie and video game

Let m = number of movies

Let v = number of video games.

We have 2 variables, so we will need to generate 2 equations to solve for them.

8 movies and 3 video games total 51 and means + Total is =

8 m + 3 v = 51

2 movies and 5 video games total 34

2m + 5v = 34

Now you can solve the system of equations with your method of choice.

I'll use substitution

2m + 5v = 34

2m = 34-5v

m = 17 - 2.5v

8 m + 3 v = 51

8(17 - 2.5v) + 3v = 51

136 - 20v + 3v = 51

85 = 17v

v = $5

m = 17 - 2.5 v

m = 17 - 2.5(5)

m = $4.5

You can check that both equations and solutions work by substituting in the numbers.

8 m + 3 v = 51

8(4.5) + 3 (5) ?= 51

51 ?= 51 yes works

2m + 5v = 34

2(4.5) + 5(5) ?= 34

34 ?= 34 Yes this works.

Hope this helps!