SOLUTION: Investments An investor owned 300 shares of an oil company and 250 shares of a movie company. The quarterly dividend from the two companies was $187.50. After the investor sold 120

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Investments An investor owned 300 shares of an oil company and 250 shares of a movie company. The quarterly dividend from the two companies was $187.50. After the investor sold 120      Log On


   



Question 1054177: Investments An investor owned 300 shares of an oil company and 250 shares of a movie company. The quarterly dividend from the two companies was $187.50. After the investor sold 120 shares of the oil company and bought an additional 120 shares of the movie company, the quarterly dividend became $211.50.
Find the dividend per share for each stock.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the quarterly dividend
from 1 share of the oil company
Let +b+ = the quarterly dividend
from 1 share of the movie company
-----------------------------------
(1) +300a+%2B+250b+=+187.5+
-------------------------------
+300+-+120+=+180+
+250+%2B+120+=+370+
------------------------------
(2) +180a+%2B+370b+=+211.5+
------------------------------
Divide both sides of (1) and (2) by +25+
(1) +12a+%2B+10b+=+7.5+
(2) +7.2a+%2B+14.8b+=+8.46+
------------------------------
Multiply both sides of (1) by +10+
Multiply both sides of (2) by +100+
(1) +120a+%2B+100b+=+75+
(2) +720a+%2B+1480b+=+846+
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Multiply both sides of (1) by +6+
and subtract (1) from (2)
(2) +720a+%2B+1480b+=+846+
(1) +-720a+-++600b+=+-450+
------------------------------
+880b+=+396+
+b+=+.45+
and
(1) +120a+%2B+100b+=+75+
(1) +120a+%2B+100%2A.45+=+75+
(1) +120a+=+75+-+45+
(1) +120a+=+30+
(1) +a+=+.25+
-------------------
The quarterly dividend
from 1 share of the oil company
= $.25
The quarterly dividend
from 1 share of the movie company
= $.45
-----------------------------------
check answer:
(1) +300a+%2B+250b+=+187.5+
(1) +300%2A.25+%2B+250%2A.45+=+187.5+
(1) +75+%2B+112.5+=+187.5+
(1) +187.5+=+187.5+
and
(2) +180a+%2B+370b+=+211.5+
(2) +180%2A.25+%2B+370%2A.45+=+211.5+
(2) +45+%2B+166.5+=+211.5+
(2) +211.5+=+211.5+
OK