Question

A person has 43,000 invested un stock A and stock B. Stock A currently sells for $30 a share abd stock B sells for $80 a share. If stock B doubles in value and stock a goes up 50% his stock will be worth $84,000. How many shares of each stock does he own?

Answer 1

First, define variables as follows :-

Let x = number of shares of stock A

Let y = number of shares of stock B

Now, use the information given to set up equations

price of stock A + price of stock B = $43,000

Double the price of stock B + (the price of stock A + 50%) = $84,000

price of stock A = shares of A * price per share = x * 30= 30x

price of stock B = shares of B * price per share = y * 80 = 80y

double the price of stock B = 80*2 = 160

the price of stock A + 50% = 30+ .5(30) = 45

Using this, we get these two equations:

30x + 80y = 43,000

45x + 160y = 84,000

Now, we can solve the system of equations for x and y.

First, multiply the first equation by -2 and add it to the second to eliminate y.

-2(30x + 80y =43,000)

=> -60x - 160y = -86,000

-60x - 160y = -86,000

+45x + 160y = 84,000

___________________

-60x + 45x = -2,000

15x=2000

Next, divide each side by 15 to isolate x.

x = 2000/15

x = 133.333

Next, plug x into either one of the initial equations to find y.

30(133.333) + 80y = 43,000

4000 +80y = 43,000

subtract 4,000 from each side

80y = 39,000

divide both sides by 80 to isolate y

y = 487.5

Finally, we get

He owns 133 shares of stock A and 487 shares of stock B.

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