Question

Hardly received some gift cards from music and movie downloads for her birthday using one of them she downloads 20 songs and 20 movies which cost a total of $240 using another she purchased 19 song and 13 movies which cost a total of $168 how much does each download cost downloads cause blank for a song and blink for a movie

Answer 1

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:

1. From the first transaction (20 songs and 20 movies for $240):
\[
20x + 20y = 240
\]

2. 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**