One month Boris rented 2 movies and 5 video games for a total of $30. The next month he rented 8 movies and 3 video games for a total of $35. Find the rental cost for each movie and each video game.
Let's use variables to represent the rental cost for a movie and a video game. Let's call the cost for a movie "m" and the cost for a video game "v".
From the first month, we know that:
2m + 5v = 30
From the second month, we know that:
8m + 3v = 35
We now have two equations with two variables. We can use elimination or substitution to solve for "m" and "v".
Let's use elimination. We can multiply the first equation by 3 and the second equation by -5, so that we can eliminate "v":
6m + 15v = 90
-40m - 15v = -175
Adding the two equations gives:
-34m = -85
Dividing both sides by -34 gives:
m ≈ 2.50
Now we can substitute this value back into one of the original equations to solve for "v". Let's use the first equation:
2(2.50) + 5v = 30
5v = 25
v = 5
Therefore, the rental cost for each movie is $2.50 and the rental cost for each video game is $5.
Let's assume the cost of renting a movie is "m" dollars and the cost of renting a video game is "g" dollars.
According to the given information, we can set up the following equations:
2m + 5g = 30 ----(1)
8m + 3g = 35 ----(2)
To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the method of elimination.
To eliminate the variable "g," let's multiply equation (1) by 3 and equation (2) by 5:
6m + 15g = 90 ----(3)
40m + 15g = 175 ----(4)
Now, subtract equation (3) from equation (4) to eliminate "g":
40m + 15g - (6m + 15g) = 175 - 90
34m = 85
Divide both sides of the equation by 34:
m = 85/34
m ≈ $2.50
Substitute the value of "m" back into equation (1) to find the value of "g":
2(2.50) + 5g = 30
5 + 5g = 30
5g = 30 - 5
5g = 25
g = 25/5
g = $5
Therefore, the cost of renting a movie is approximately $2.50, and the cost of renting a video game is $5.