Answer:
He bought 40 shares.
Step-by-step 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.