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 $26,880 in these stocks at the beginning of November and sold them for $22,080 3 months later, how many shares of each stock did you buy?

Hess Corp. (HES) stock  shares

Exxon Mobil (XOM) stock

Answer 1

Let the number of HES shares is 'H' and that of XOM is 'X'.

When the shares are bought, the price of one HES share is $80 and that of XOM is $96 and the total investment is $26,880.

So we can write as

80H + 96X = 26880 --------(1)

Similarly, when the shares are sold, the price of one HES share is $64 and that of XOM is $80 and the total money got is $22,080.

So,

64H + 80X = 22080 -------(2)

For simplification, divide both the equations by 16,

Then equation (1) becomes

5H + 6X = 1680 ----(3)

and equation (2) becomes

4H + 5X = 1380 -----(4)

Now, by rearranging equation (3), we can write

-------(5)

Put this equation (5) in equation (4)

ie,

Now solve this equation by expanding and multiplying with 5.

Now put this value of X in equation (5) to find H.

So the answer is

Number of Hess Corp. (HES) stock  shares = 120

Number of Exxon Mobil (XOM) stock shares = 180