(a) Explanation Given: The system of equations for two armies is provided as: Rate of increase ( Red Army ) = 200 , 000 − 0.5 r − 0.3 b Rate of increase ( Blue Army ) = 350 , 000 − 0.5 r − 0.7 b Here, r represents the number of soldiers of Red army for a given time and b represents the number of soldiers of Blue Army for the same time. Explanation: The problem assumes that the rate of increase is zero for both the armies. So, the system of equations becomes: 0 = 200 , 000 − 0.5 r − 0.3 b 0 = 350 , 000 − 0.5 r − 0.7 b Subtract 200 , 000 from the first equation and 350 , 000 from the second equation. That is, 0 − 200 , 000 = 200 , 000 − 0.5 r − 0.3 b − 200 , 000 0 − 350 , 000 = 350 , 000 − 0.5 r − 0.7 b − 350 , 000 The equations become: − 0.5 r − 0.3 b = − 200 , 000 − 0.5 r − 0.7 b = − 350 , 000 The equations are multiplied by numbers such that the coefficients of the variable r in the two equations are negatives of one another. Hence, the first equation is multiplied by 1 and the second equation by – 1 . So, the equations become: − 0.5 r − 0.3 b = − 200 , 000 0.5 r + 0.7 b = + 350 , 000 The solutions that satisfy both the equations are also the solutions for the sum of their equations. So, add the two equations. That is, − 0.5 r − 0.3 b = − 200 , 000 0 (b) To determine To describe: The meaning of the rate of increase being zero.

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

11th Edition

ISBN: 9780321931078

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 6.1, Problem 20E

(a)

To determine

The number of soldiers in each army when the rate of increase for each is zero.

(b)

To determine

To describe: The meaning of the rate of increase being zero.

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Chapter 6.1, Problem 19E

Chapter 6.1, Problem 21E

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Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

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