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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?

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gcosarinsky

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:

[tex]22,240 = A*80 + B*96[/tex]     (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:

[tex]18,080 = 64*A + 80*B[/tex]

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

[tex] A = (22,240-B*96)/80 [/tex]

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.

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