Let's denote the cost of each song as \( x \) and the cost of each movie as \( y \).
We can set up the following equations based on the information provided:
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From the first transaction (20 songs and 20 movies for $240): \[ 20x + 20y = 240 \]
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From the second transaction (19 songs and 13 movies for $168): \[ 19x + 13y = 168 \]
Now we can simplify the first equation. Dividing every term by 20 gives us: \[ x + y = 12 \quad \text{(Equation 1)} \]
Now we can use this simplified equation to solve for \( y \): \[ y = 12 - x \quad \text{(Equation 2)} \]
Next, we can substitute Equation 2 into the second equation: \[ 19x + 13(12 - x) = 168 \] Distributing the 13: \[ 19x + 156 - 13x = 168 \] Combining like terms: \[ 6x + 156 = 168 \] Subtracting 156 from both sides: \[ 6x = 12 \] Dividing by 6: \[ x = 2 \]
Now substituting \( x \) back into Equation 2 to find \( y \): \[ y = 12 - 2 = 10 \]
Thus, the cost of each download is:
- Cost of a song: \( \mathbf{2} \)
- Cost of a movie: \( \mathbf{10} \)
So, the final answer is:
- Blank for a song: $2
- Blank for a movie: $10
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