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

No shares were bought of either stock.

Step-by-step explanation:

To find the number of shares of each stock that were bought, we need to set up a system of equations.

Let's assume the number of shares of Hess Corp. (HES) stock bought is x, and the number of shares of Exxon Mobil (XOM) stock bought is y.

According to the information given:

1. The total investment in these stocks is $22,240, so we have the equation:

x($80 per share) + y($96 per share) = $22,240

1. The total value of the stocks sold 3 months later is $18,080, so we have the equation:

x($64 per share) + y($80 per share) = $18,080

We can now solve this system of equations using substitution or elimination.

Let's use elimination:

1. Multiply the first equation by 64 and the second equation by 80 to eliminate the x terms.

64x + 64y = 64($22,240)

80x + 80y = 80($18,080)

1. Subtract the first equation from the second equation to eliminate the x terms.

(80x + 80y) - (64x + 64y) = 80($18,080) - 64($22,240)

1. Combine like terms.

16x + 16y = $1,444,800 - $1,421,760

16x + 16y = $23,040

1. Divide the equation by 16 to solve for y.

y = $23,040 ÷ 16

y = $1,440

1. Substitute the value of y back into either of the original equations to solve for x.

x($80 per share) + $1,440($96 per share) = $22,240

x($80 per share) + $138,240 = $22,240

x = ($22,240 - $138,240) ÷ $80

x = -$116,000 ÷ $80

x = -$1,450

Since the number of shares cannot be negative, we can conclude that the correct answer is that no shares were bought.

Answer 2

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.