Concept explainers
Stock Portfolio An investor owns three stocks: A, B, and C. The closing prices of the stocks on three successive trading days are given in the table.
Despite the volatility in the stock prices, the total value of the investor’s stocks remained unchanged at $74,000 at the end of each of these three days. How many shares of each stock does the investor own?
The number of shares of each stock owned by investor.
Answer to Problem 45E
The number of shares of Stock A own by investor is 1,500, Stock B is 1,200 and Stock C is 1,000.
Explanation of Solution
Given:
The total value of the investor’s stocks remained unchanged at the end of each day is
At the end of Monday the closing prices of Stock A is
At the end of Tuesday the closing prices of Stock A is
At the end of Wednesday the closing prices of Stock A is
Calculation:
Let the number of shares of Stock A own by investor is x,
The number of shares of Stock B own by investor is y and,
The number of shares of Stock C own by investor is z.
To get the number of shares of each stock own by investor, convert all the facts into equation.
The closing prices at the end of Monday are
The closing prices at the end of Tuesday are
The closing prices at the end of Wednesday are
The system of equations is,
To get the solution of system eliminate term y from equation (2) and terms x and y from equation (3).
Multiply equation (1) by
That is,
Multiply equation (2) by 5,
That is,
Add equation (5) and (4) to eliminate terms x from equation (2) as the coefficients of x-terms in both equations are negative of each other,
That is,
The equation (6) is new equation (2) for triangular system.
Multiply equation (1) by
That is,
Multiply equation (3) by 5,
That is,
Add equation (8) and (7) to eliminate terms x from equation (3) as the coefficients of x-terms in both equations are negative of each other,
That is,
Multiply equation (6) by
That is,
Multiply equation (9) by 2,
That is,
And add equation (11) and (10) to eliminate terms y from equation (3) as the coefficients of y-terms in both equations are negative of each other,
That is,
The equation (12) is new equation (3) for triangular system.
Thus, the triangular system is,
Substitute 1,000 for z into equation (6) to get the value of y,
Substitute 1,200 for y and 1,000 for z into equation (1) to get the value of y,
The value of x is 1,500, y is 1,200 and z is 1,000.
Therefore, the number of shares of Stock A own by investor is 1,500, Stock B is 1,200 and Stock C is 1,000.
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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