Question

In the 3-month period November 1, 2014, through January 31, 2015, Hess Corp. (HES) stock decreased from $80 to $64 per share, and Exxon Mobil (XOM) stock decreased from $96 to $80 per share.† If you invested a total of $22,240 in these stocks at the beginning of November and sold them for $18,080 3 months later, how many shares of each stock did you buy?

Answer 1

Answer: 170 HES and 90 XOM

Hi! Let's say you bought A HES shares, and B XOM shares. As you invested $22,240, yo have that:

$22,240 = A*80 + B*96$     (80 and 96 are the initial prices)

3 months later those prices decreased to 64 and 80, and you sold your shares at those prices, then:

$18,080 = 64*A + 80*B$

This is a system of two linear equations and two unkowns A, B. You can solve it getting A from first equation:

$A = (22,240-B*96)/80$

And then replacing A into the second equation you can find the value of B. Then replacing B in the third equation you get A.