MATH SOLVE

4 months ago

Q:
# 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!

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!