Sure, let's break down the solution step by step:
1. First, we are given that the video store sells a certain video for $32, which is 60% more than it costs the store to purchase the video. To find out the store's cost, we set up an equation:
$32 = 1.6x
Here, x represents the cost to the store. We multiply the store's cost by 1.6 because 1.6 is the decimal equivalent of 160%, which represents a 60% increase.
Solving for x, we divide both sides of the equation by 1.6:
x = $32 / 1.6 = $20
So, the store's cost for the video is $20.
2. During the inventory sale, the store offers employees a 25% discount off the store's cost. To find the employee's purchase price, we multiply the store's cost by 0.75 (since 100% - 25% = 75%):
Employee's purchase price = 0.75 * $20 = $15
Therefore, the employee would pay $15 for the video during the sale.
3. Finally, the question asks for the employee's purchase price as a percentage of the original price the store charged. To calculate this, we divide the employee's purchase price ($15) by the original price ($32) and multiply by 100:
Price percentage = ($15 / $32) * 100 = 46.875%
You can round this percentage to either 46.8% or 46.9% as mentioned in the book's answer.
So, the employee's purchase price is approximately 46.9% of the price the store originally charged for the video.