Question

EBay is a popular website where people sell or auction off just about anything. The final purchase price at the end of an auction is called a “closing bid.” In the fall of 2006, the Sony Playstation 3 (PS3) sold out in stores across America in less than five minutes after each store opened. Many people sold these PS3’s on eBay.
The original sales price for the PS3 was approximately $600. One lucky seller on eBay sold a PS3 for over $10,000 the day it was released. However, the mean closing bid for a PS3 on eBay that first day (Day 0) was approximately $5,500. Each day after the release, the average price of the closing bid decreases by $250. Ignore costs such as tax and shipping and answer the following questions.

A: Find the linear equation for the mean closing bid in the form y = mx + b.
B: What is the minimum amount the PS3 could sell for and the seller still make a profit?
C: How many days would the PS3 have to be on eBay before there is no profit for the seller?

Answer 1

Answer:

a)y = -250x +5500

b)  selling price > 600

c) After 19 days, the seller will no longer make a profit

Step-by-step explanation:

a)The original price is 5500.  That is the y intercept or (b) in the equation y = mx+b.  It decreases 250 each day.  That means  the slope is -250 (or m)

The slope intercept form of the equation is

y = -250x +5500

b)  The price was 600  when purchased so the seller must sell if for more than that to make a profit

selling price > 600

c) to determine when the seller would no longer make a profit

the cost must be less than or equal to 600

-250x +5500 ≤ 600

Subtract 5500 from each side

-250x +5500-5500 ≤ 600-5500

-250x ≤-4900

Divide each side by -250, remembering to flip the inequality sign

-250x/-250 ≥-490-/-250

x ≥19.6

After 19 days, the seller will no longer make a profit