Let's use a system of equations to solve for the rental cost of a movie (let's call it \( m \)) and a video game (let's call it \( g \)).
From the information provided:
-
For the first month, Sam rented movies and video games for a total of $32: \[ m + 3g = 32 \quad \text{(1)} \]
-
For the second month, Sam rented 12 movies and 2 video games for a total of $29: \[ 12m + 2g = 29 \quad \text{(2)} \]
Now, we can solve this system of equations. First, let's simplify equation (2) by dividing everything by 2: \[ 6m + g = 14.5 \quad \text{(3)} \]
Now we can express \( g \) from equation (3): \[ g = 14.5 - 6m \quad \text{(4)} \]
Next, we'll substitute the value of \( g \) from equation (4) into equation (1): \[ m + 3(14.5 - 6m) = 32 \] \[ m + 43.5 - 18m = 32 \] \[ -17m + 43.5 = 32 \] \[ -17m = 32 - 43.5 \] \[ -17m = -11.5 \] \[ m = \frac{11.5}{17} \] \[ m = 0.6765 \quad \text{(approximately)} \]
Now, substitute \( m \) back into equation (4) to find \( g \): \[ g = 14.5 - 6(0.6765) \] \[ g = 14.5 - 4.059 \] \[ g = 10.440 \quad \text{(approximately)} \]
Since neither value seems to match the possible options provided, let's try each option to see which fits both equations.
A. \( m = 4.50, g = 2.50 \)
- \( 4.50 + 3(2.50) = 4.50 + 7.50 = 12.00 \) (Not equal to 32)
- \( 12(4.50) + 2(2.50) = 54 + 5 = 59 \) (Not equal to 29)
B. \( m = 1.00, g = 6.00 \)
- \( 1 + 3(6) = 1 + 18 = 19 \) (Not equal to 32)
- \( 12(1) + 2(6) = 12 + 12 = 24 \) (Not equal to 29)
C. \( m = 2.50, g = 4.50 \)
- \( 2.50 + 3(4.50) = 2.50 + 13.50 = 16.00 \) (Not equal to 32)
- \( 12(2.50) + 2(4.50) = 30 + 9 = 39 \) (Not equal to 29)
D. \( m = 1.50, g = 5.50 \)
- \( 1.50 + 3(5.50) = 1.50 + 16.50 = 18.00 \) (Not equal to 32)
- \( 12(1.50) + 2(5.50) = 18 + 11 = 29 \) (Equal to 29)
From these calculations, it looks like none of the options satisfies both conditions.
This is an unexpected result. Can you confirm the totals or rental quantities for movies and video games?
1 answer