Question

Stock Portfolio You invested a total of $25,000 in Coca-
Cola Company and Intel Corporation. You purchased Coca-
Cola at $45 per share and Intel at $32 per share. Ir Coca-Cola
doubles in value and Intel stock goes up by 50%, your portfo-
lio will be worth $42.000. How many shares of each stock do
you own?

Answer 1

Let x and y be the number of Coca-Cola and Intel shares, respectively.

You initial investment was

$45x+32y=25000$

In the forecast, we have that Coca-Cola shares double in value, and thus they're worth 90 dollars. Similarly, Intel shares increase by half of their current value, raising to 32+16=48. So, your new portfolio is

$90x+48y=42000$

At this point we can solve the linear system given by the two equations: we can multiply the first equation by 2 to get

$90x+64y=50000$

Subtracting the second equation from this one we have

$(64-48)y=50000-42000 \iff 16y=8000 \iff y=500$

So, you own 500 Intel shares. Plug this value into one of the equations (for example, the first) to solve for x, i.e. the number of Coca-Cola shares:

$45x+32\cdot 500=25000 \iff x=\dfrac{25000-32\cdot 500}{45}=200$