Ed bought $2,000 in stock shares one week before the stock price dropped $10.00. If he had waited for the price setback, he could have bought 10 more shares f or the same amount. How many shares did he buy?1.)402.)503.)60
Accepted Solution
A:
The Answer is 1: 40 Shares
Proof: In week 1, Ed purchased stock: x = number of shares of stock he bought p = purchase price per share xp = 2000 One week later...the stock tumbled. Price is now (p-10) He could have bought 10 more shares: (x+10) for the same purchase price (x+10)(p-10)=2000 since x*p = 2000 x = 2000/p p = 2000/x (x+10)(p-10) = 2000 xp -10x +10p -100 = 2000 substitute for x (2000/p)*p - 10*(2000/p) +10p -100 = 2000 2000 -20000/p +10p -100 = 2000 -20000/p +10p = 100 multiply by p -20000 + 10p^2 = 100p 10p^2 -100p - 20000 = 0 divide by 10 p^2 -10p - 2000 = 0 factor 20*100 = 2000 < 40*50 = 2000 < . (p-50)(p+40) = 0 p = 50 or -40, but a negative stock price is nonsense. p = 50 x = 2000/p x = 40 So, in week 1, Ed purchased 40 shares at $50 per share. The next week the stock fell by $10 Now the price is $40. For $2000 he could buy 50 shares now. Which are 10 more shares than he bought the first week!