Question

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 for the same amount. How many shares did he buy?

Answer 1

Answer:

He bought 40 shares.

Explanation:

Step 1: Determine the initial stock price

Use the expression below to determine the total initial stock price as shown;

T=S×s

where;

T=total initial stock price

S=initial stock price per share

s=number of shares

In our case;

T=$2,000

S=x

s=unknown

replacing;

2,000=x×s

s=2,000/x

Step 2: Determine the final stock price

Use the expression below;

F=f×s2

where;

F=final stock price=$2,000

f=final stock price per stock=(x-10)

s2=final number of shares bought=(2,000/x)+10

replacing;

2,000=(x-10){(2,000/x)+10)

2,000=x(2,000/x)+(10 x)-10(2,000/x)-100

(2,000=2,000+10 x-20,000/x-100)x

2,000 x=2,000 x+10 x²-20,000-100 x

2,000 x-2000 x=10 x²-100 x-20,000

10 x²-100 x-20,000=0

solving quadratically;

x=[100±√{100²-(4×10×-20,000)}]/(2×10)

x={100±√(10,000+800,000)}/20

x=(100±900)/20

x=1,000/20=50

Initial stock price=$50

Number of shares bought=2,000/x=2,000/50=40

He bought 40 shares.