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3 years ago

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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, an

d 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?

1 answer:

Anit [1.1K]3 years ago

8 0

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.

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Negative exponent rule: When an exponent is negative, you can make it positive by making the base a fraction. When the number is apart of a bigger fraction, you can move it to the other side (top/bottom). $a^{-x} = \frac{1}{a^{x}}$ , and to help with this question: $\frac{a^{-x}b}{1} = \frac{b}{a^{x}}$ .

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$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)}q^{(1/3)}}{p^{(4)}}$ Rearranged for you to see the like terms

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)+(1/3)}}{p^{(4)}}$ Multiplying exponents with same base

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Here is a version in pen if the steps are hard to see.

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