Question

A person has 14000 invested in stock A and stock B. A currently sells for $40 a share and stock B sells for 60 a share. If stock B doubles in value and stock A goes up 50%, his stock will be worth 24,000. How many shares of each stock does he own?

Answer 1

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.

$40x+60y=14000$

Divide both sides by 20.

$2x+3y=700$            .... (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

$60x+120y=24000$

Divide both sides by 60.

$x+2y=400$            .... (2)

Solve equation (1) and (2) by elimination method.

Multiply 2 on both sides in equation (2).

$2x+4y=800$       .... (3)

Subtract equation (3) from equation (1).

$2x+3y-2x-4y=700-800$

$-y=-100$

$y=100$

The value of y is 100.

Substitute y=100 in equation (1).

$2x+3(100)=700$

$2x+300=700$

Subtract 300 from both sides.

$2x=700-300$

$2x=400$

Divide both sides by 2.

$x=200$

The value of x is 200.

Therefore he own 200 shares of stock A and 100 shares of stock B.