16. Last year, Andrea bought 85 songs from an online company for a total of $96.90. Each song cost $ 1.09 plus tax.

Question

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