Find the rental cost for each movie and each video game

Question

One month alan rented 12 movies and 2 video games for a total of $41. The next month he rented 3 movies and 5 video games for a total of $35. Find the rebtal cost for each movie and each video game.

Answer 1

Let x be the rental cost of a movie and y be the rental cost of a video game. This provides us with a system of two equations and two unknowns:

12 x + 2y = 41

3x + 5y = 35

multiply 2nd row by 4

12 x + 2y = 41

12x +20y = 140

subtract 2nd row from 1st row

-18y = --99

y = 5.5 --> video game cost 5.50 each to rent

plug value for y back into first equation to solve for x:

12x + 2(5.5) = 41

12x + 11 = 41

12x = 30

x = 2.5 --> movie cost 2.50 each to rent

Answer 2

This will require a series of equations.

M for movies and v for video games as variables

12m + 2v = $41

3m + 5v = $35

The goal is to cancel out one of the variables until everything is in terms of one variable. it’s easiest to get rid of m in this case, since you only have to multiple the bottom equation by -4

12m + 2v = $41

-4(3m + 5v = $35)

12m + 2v = $41

-12m - 20v = -140

Now add the equations together and solve for v

-18v = -99

v = $5.5

Plug the value of v into either original equation to find cost of movies. Hope that helped