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

He own 200 shares of stock A and 100 shares of stock B.

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.