Answer:
$2.25 and $6.25
Explanation:
To find the rental cost for each movie and each video game, we can set up a system of equations based on the given information.
Let's assume the rental cost for each movie is "m" and the rental cost for each video game is "v".
From the first month's rental, we have the equation:
2m + 6v = 42
From the second month's rental, we have the equation:
5m + 3v = 30
To solve this system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
Step 1: Solve one equation for one variable in terms of the other variable.
From the first equation, we can solve for m:
2m = 42 - 6v
m = (42 - 6v) / 2
m = 21 - 3v
Step 2: Substitute the expression for m in the second equation.
5(21 - 3v) + 3v = 30
Step 3: Simplify and solve for v.
105 - 15v + 3v = 30
-12v = -75
v = 75 / 12
v ≈ 6.25
Step 4: Substitute the value of v back into either equation to solve for m.
Using the first equation:
2m + 6(6.25) = 42
2m + 37.5 = 42
2m = 42 - 37.5
2m = 4.5
m = 4.5 / 2
m = 2.25
Method 2: Elimination
Step 1: Multiply the first equation by 5 and the second equation by 2 to eliminate the m variable.
10m + 30v = 210
10m + 6v = 60
Step 2: Subtract the second equation from the first equation to eliminate the m variable.
(10m + 30v) - (10m + 6v) = 210 - 60
24v = 150
v = 150 / 24
v ≈ 6.25
Step 3: Substitute the value of v back into either equation to solve for m.
Using the first equation:
2m + 6(6.25) = 42
2m + 37.5 = 42
2m = 42 - 37.5
2m = 4.5
m = 4.5 / 2
m = 2.25
Therefore, the rental cost for each movie is approximately $2.25 and the rental cost for each video game is approximately $6.25.