Respuesta :
Answer:
He own 200 shares of stock A and 100 shares of stock B.
Step-by-step explanation:
Let x be the number of shares of stock A and y be the number of shares of stock B.
Current value of a share of stock A = $40
Current value of a share of stock B = $60
A person has 14000 invested in stock A and stock B.
[tex]40x+60y=14000[/tex]
Divide both sides by 20.
[tex]2x+3y=700[/tex] .... (1)
Stock B doubles in value and stock A goes up 50%, his stock will be worth 24,000.
New value of a share of stock A = $40 + (50% of 40)= $40 + $20 = $60
New value of a share of stock B = $60 × 2 = $120
[tex]60x+120y=24000[/tex]
Divide both sides by 60.
[tex]x+2y=400[/tex] .... (2)
Solve equation (1) and (2) by elimination method.
Multiply 2 on both sides in equation (2).
[tex]2x+4y=800[/tex] .... (3)
Subtract equation (3) from equation (1).
[tex]2x+3y-2x-4y=700-800[/tex]
[tex]-y=-100[/tex]
[tex]y=100[/tex]
The value of y is 100.
Substitute y=100 in equation (1).
[tex]2x+3(100)=700[/tex]
[tex]2x+300=700[/tex]
Subtract 300 from both sides.
[tex]2x=700-300[/tex]
[tex]2x=400[/tex]
Divide both sides by 2.
[tex]x=200[/tex]
The value of x is 200.
Therefore he own 200 shares of stock A and 100 shares of stock B.
