Some of the following exercises have nonunique solutions. 43. Investment A brokerage house offers three stock port-folios for its clients. Portfolio I consists of 10 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. Portfolio II consists of 12 blocks of common stock, 8 municipal bonds, and 5 blocks of preferred stock. Portfolio III consists of 10 blocks of common stock, 6 municipal bonds, and 4 blocks of preferred stock. A client wants to combine these portfolios so that she has 180 blocks of common stock, 140 municipal bonds, and 110 blocks of preferred stock. Can she do this? To answer this question, let x equal the number of units of portfolio I, y equal the number of units of portfolio II, and z equal the number of units of portfolio III, so that the equation 10 x + 12 y + 10 z = 180 represents the total number of blocks of common stock. a. Write the remaining two equations to create a system of three equations. b. Solve the system of equations, if possible.
Some of the following exercises have nonunique solutions. 43. Investment A brokerage house offers three stock port-folios for its clients. Portfolio I consists of 10 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. Portfolio II consists of 12 blocks of common stock, 8 municipal bonds, and 5 blocks of preferred stock. Portfolio III consists of 10 blocks of common stock, 6 municipal bonds, and 4 blocks of preferred stock. A client wants to combine these portfolios so that she has 180 blocks of common stock, 140 municipal bonds, and 110 blocks of preferred stock. Can she do this? To answer this question, let x equal the number of units of portfolio I, y equal the number of units of portfolio II, and z equal the number of units of portfolio III, so that the equation 10 x + 12 y + 10 z = 180 represents the total number of blocks of common stock. a. Write the remaining two equations to create a system of three equations. b. Solve the system of equations, if possible.
Solution Summary: The author explains that the system of three equations is inconsistent and has no solution.
Some of the following exercises have nonunique solutions.
43. Investment A brokerage house offers three stock port-folios for its clients. Portfolio I consists of 10 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. Portfolio II consists of 12 blocks of common stock, 8 municipal bonds, and 5 blocks of preferred stock. Portfolio III consists of 10 blocks of common stock, 6 municipal bonds, and 4 blocks of preferred stock. A client wants to combine these portfolios so that she has 180 blocks of common stock, 140 municipal bonds, and 110 blocks of preferred stock. Can she do this? To answer this question, let x equal the number of units of portfolio I, y equal the number of units of portfolio II, and z equal the number of units of portfolio III, so that the equation 10x + 12y + 10z = 180 represents the total number of blocks of common stock.
a. Write the remaining two equations to create a system of three equations.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY