SOLUTION: An investor owned 300 shares of an oil company an 200 shares of a movie company. The quarterly dividend from the two stocks was $165. After the investor sold 100 shares of the oil

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Question 83089This question is from textbook introductory algebra
: An investor owned 300 shares of an oil company an 200 shares of a movie company. The quarterly dividend from the two stocks was $165. After the investor sold 100 shares of the oil company and bought an additional 100 shares of the movie company, the quarterly dividend became $185. Find the dividend per share for each stock. This question is from textbook introductory algebra

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Let P represent the dividend per share of the Oil company (P for petroleum) and let M
represent the dividend per share of the Movie company.
.
Since the original investment was 300 shares of the Oil company, the total amount of the
dividend that it produced was 300 times P or 300P. And since the original investment
in the Movie company was 200 shares and each share returned M, the total amount of the dividend
that this investment produced was 200 times M or 200M. The problem tells you that when these
are added together, the total is $165 for the quarter. In equation form this becomes:
.
300P + 200M = 165
.
Next the problem tells you that the investor sells 100 shares of the Oil company.
That means that there are now 300 minus 100 ... or 200 shares of the Oil company.
And further, the investor buys 100 shares of the Movie company, so there are now 200 plus
100 or 300 shares of it.
.
The Oil company portion of the dividend is now 200 times P or 200P and the Movie company
portion now produces 300 times M or 300M. The problem tells you that the sum of these two
dividends is now $185. In equation form this is:
.
200P + 300M = 185
.
Write these two equations together:
.
300P + 200M = 165
200P + 300M = 185
.
There are several ways that these two equations can be solved. Let's use variable
elimination. The object of this method is to make either the P terms in both equations
equal or make the M terms in both equations equal. Let's make the P terms equal.
Suppose we multiplied all terms on both sides of the top equation by 2. If we did, the top
equation would become:
.
600P + 400M = 330
.
Now suppose we multiplied all terms on both sides of the bottom equation by 3. This
multiplication would make the bottom equation become:
.
600P + 900M = 555
.
So now the equation set has been converted to:
.
600P + 400M = 330
600P + 900M = 555
.
Now suppose that we in each column of the equations we subtracted the bottom equation
from the top equation. Notice that in the first column we subtract 600P from 600P and
this makes the P terms disappear. In the second column we subtract 900M from 400M and
the result is -500M. And on the right side we subtract 555 from 330 and the result of
that subtraction is -225. So the single equation that we are left with after subtracting
is:
.
-500M = -225
.
Solve for M by dividing both sides of this result by -500 which is the multiplier
of M. When you do that division you get:
.
M+=+-225%2F-500+=+0.45
.
So the per share dividend of the Movie company is $0.45 or 45 cents per share.
.
Now that you know that you can return to either one of the original equations and
substitute 0.45 for M and solve for P. Let's return to the first equation and solve for P.
.
The first equation was:
.
300P + 200M = 165
.
Substitute 0.45 for M and this equation becomes:
.
300P + 200(0.45) = 165
.
But 200(0.45) equals 90. So after this multiplication the equation is:
.
300P + 90 = 165
.
Get rid of the 90 on the left side by subtracting 90 from both sides to get:
.
300P = 75
.
Finally, solve for P by dividing both sides of this equation by 300 to get:
.
P+=+75%2F300+=+0.25
.
This tells you that the per share dividend of the Oil company is $0.25 or 25 cents.
.
So the answers are that the Oil company dividends are 25 cents per share and the Movie company
dividends are 45 cents per share. Those are the answers you were asked to find.
.
You can do a check by substituting these two values into the second of the original
equations to see if they satisfy the equation. The second equation was:
.
200P + 300M = 185
.
Substituting results in:
.
200(0.25) + 300(0.45) = 185
.
Multiplying out the two terms on the left side gives you:
.
50 + 135 = 185
.
And since the left side equals the right side, this equation is satisfied by the two values
that you found. This helps to confirm that the two answers are correct.
.
Hope this helps you to understand the problem a little better.