A video store sells a certain video for $32, which is 60 percent more than it costs the store to purchase this video. During an inventory sale, employees are invited to purchase remaining videos at 25 percent off the store's cost. If an employee purchases this video during the sale, the employee's purchase price would be what percent of the price the store originally charged for the video?
Here's the book answer: First your told that a store sells a certain video for $32, which is 60 percent more than it costs the store. So to figure out the store's cost, translate the English into math: 32=1.6x, where x is the cost to the store. x=32/1.6=20, so the store's cost is $20. During a sale it's offered to employees at 25 percent off the store's cost, or .75*$20=$15, so $15 is the final price to the employee. But wait! the question asks what percent of the original price the employee pays, so divide 15 by 32. You should get .46875, or 46.875 percent, which you can grid as either 46.8 or 46.9.
My question is: Where did they get 1.6x from and how did they get .75*$20 from? And I really don't understand the answer so help me.
1.6 is the decimal equivalent of 160%. The store charged customers 160% of its wholesale price. 1.6x is 160% of an unknown number (the store's wholesale price).
.75*$20 is 75% of the store's cost of $20. 100% - 25% = 75%
explain how they got the whole answer. Because what you just explained to me is'nt enough.
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.