Question

16. Last year, Andrea bought 85 songs from an online company for a total of $96.90. Each song cost $ 1.09 plus tax.
Part A
Which equation can be used to determine the amount of tax, x, in dollars, that Andrea paid for each song?
Responses


85(1.09) + x =96.90


85x + 1.09 = 96.90


85 (1.09 + x) = 96.90


X (85 + 1.09) = 96.90
Part B
How much tax, in dollars, did Andrea pay for each song?
Enter your answer in the box.
$?

Answer 1

To solve the problem, let's break it down into parts.

### Part A

We know:

- Andrea bought 85 songs.
- Each song costs $1.09 plus tax.
- The total cost is $96.90.

For each song, the price including tax can be represented as \( 1.09 + x \), where \( x \) is the amount of tax.

So, the total cost for 85 songs can be represented as:
\[
85 (1.09 + x) = 96.90
\]

Thus, the correct equation to determine the amount of tax, \( x \), that Andrea paid for each song is:
**85 (1.09 + x) = 96.90**

### Part B

Now, let's determine the amount of tax Andrea paid for each song.

First, we can use the equation we derived to solve for \( x \):

1. Expand the equation:
\[
85(1.09) + 85x = 96.90
\]

2. Calculate the total cost of the songs without tax:
\[
85(1.09) = 92.65
\]

3. Substitute this value back into the equation:
\[
92.65 + 85x = 96.90
\]

4. Subtract 92.65 from both sides to isolate the term with \( x \):
\[
85x = 96.90 - 92.65
\]
\[
85x = 4.25
\]

5. Divide both sides by 85 to solve for \( x \):
\[
x = \frac{4.25}{85}
\]
\[
x = 0.05
\]

So, the amount of tax Andrea paid for each song is:
**$0.05**

### Final Answers
- Part A: **85 (1.09 + x) = 96.90**
- Part B: **$0.05**