Let's denote the rental cost of each movie as \( m \) and the rental cost of each video game as \( v \).
We can set up the following system of equations based on the information provided:
-
For the first month: \[ 12m + 2v = 31 \]
-
For the second month: \[ 3m + 5v = 37 \]
Now we can solve this system of equations.
Step 1: Simplify the first equation. We can divide the first equation by 2 to make it simpler: \[ 6m + v = 15.5 \quad \text{(Equation 1)} \]
Step 2: Rearrange Equation 1 to express \( v \): \[ v = 15.5 - 6m \quad \text{(Equation 2)} \]
Step 3: Substitute Equation 2 into the second equation: Substituting \( v \) in the second equation: \[ 3m + 5(15.5 - 6m) = 37 \] Expand this: \[ 3m + 77.5 - 30m = 37 \] Combine like terms: \[ -27m + 77.5 = 37 \] Subtract 77.5 from both sides: \[ -27m = 37 - 77.5 \] \[ -27m = -40.5 \]
Step 4: Solve for \( m \): \[ m = \frac{-40.5}{-27} = \frac{40.5}{27} = \frac{135}{90} = \frac{15}{10} = 1.5 \] So, \( m = 1.5 \).
Step 5: Find \( v \) using Equation 2: Substituting \( m = 1.5 \) back into \( v \) equation: \[ v = 15.5 - 6(1.5) \] Calculate: \[ v = 15.5 - 9 = 6.5 \] So, \( v = 6.5 \).
Finally, we find the rental costs:
- The rental cost for each movie \( m = 1.5 \) (or $1.50).
- The rental cost for each video game \( v = 6.5 \) (or $6.50).
Thus, the rental cost for each movie is $1.50 and for each video game is $6.50.
1 answer