Kevin rented some movies and video games last month. He did the same this month. The table below shows the number of movies and video games he rented each month. It also shows the total cost (in dollars).
Number of
movies 8 and 2
Number of
video games 3 and 5
Total cost
(in dollars) 27 and 28
Last
month 8,3 and 27
This
month 2,5 and 28
Let be the cost (in dollars) of renting a movie.
Let be the cost (in dollars) of renting a video game.
(a) Write a system of equations that could be used to find the rental cost (in dollars) for each movie and each video game.
(b) How much did it cost (in dollars) to rent each movie and each video game?
(a) Let x be the cost (in dollars) of renting a movie and y be the cost (in dollars) of renting a video game.
From the table, we can form the following system of equations:
8x + 3y = 27
2x + 5y = 28
(b) To solve this system of equations, we can use the method of elimination or substitution.
Using the method of elimination, we can multiply the first equation by 2 and the second equation by 8 to eliminate x:
16x + 6y = 54
16x + 40y = 224
Subtracting the first equation from the second equation, we get:
34y = 170
y = 5
Substituting y = 5 into the first equation, we get:
8x + 3(5) = 27
8x + 15 = 27
8x = 12
x = 1.5
Therefore, it cost $1.50 to rent each movie and $5 to rent each video game.