Question

A jewelry store has two options for applying a discount to bracelets that go on sale. Option 1 : Decrease the price of the bracelet by 10% each month. Option 2 : Decrease the price of the bracelet by $20 each month. Which function shows the difference in price between option 1 and option 2 for a bracelet that originally costs $100, where x is the number of months?

Answer 1

Explanation:

Let's denote the price difference between Option 1 and Option 2 as D(x), where x represents the number of months.

In Option 1, the price of the bracelet decreases by 10% each month. Therefore, the price after x months can be calculated as:

Price after x months = $100 - (10% of $100) * x

Price after x months = $100 - ($100 * 0.10) * x

Price after x months = $100 - $10x

In Option 2, the price of the bracelet decreases by $20 each month. Therefore, the price after x months can be calculated as:

Price after x months = $100 - ($20 * x)

Price after x months = $100 - $20x

To find the difference in price between Option 1 and Option 2, we subtract the price of Option 2 from the price of Option 1:

D(x) = ($100 - $10x) - ($100 - $20x)

D(x) = $100 - $10x - $100 + $20x

D(x) = $10x

So, the function that shows the difference in price between Option 1 and Option 2 for a bracelet that originally costs $100, where x is the number of months, is D(x) = $10x.