Explanation Given Information: John O’Hagan went to assisting his son Billy-Sean in his lunch break. He is facing problems with the course schedule due to a very complicated bulletin of Suburban State University. The bulletin reads as follows: The candidates must select a total of 124 credits from the sciences, Fine arts, Liberal arts and Mathematics for the degree of Bachelor of Science. There should be equal number of Fine arts and Science credits. There should be twice the number of mathematics credits as science and Fine Arts both combined, with Liberal arts credits more than the Mathematics credits by exactly one third the number of Fine Arts credits. Formula Used: Elementary row operations: Type 1: Replacing the row R i by a R i , where a is a nonzero number. Type 2: Replacing the row R i by a R i ± b R j , where a is a nonzero number. Gauss Jordan reduction method: Step 1: First clear the fractions or decimals if any. Step 2: Pivot the first nonzero element of the first row. Step 3: Use the pivot to clear its column. Step 4: Pivot the first nonzero element in the second row and clear the column. Step 5: Pivot the first nonzero element in the third row and clear the column. Step 6: Turn all the pivot elements into a 1. Calculation: Firstly identify and label the unknowns. Considering the provided information the unknowns should be labelled like this, x = Number of credits of liberal arts y = Number of credits of sciences z = Number of credits of Fine arts w = Number of credits of Mathematics It is known that he can select a total of 124 credits from all the subjects combined.. x + y + z + w = 124 Also, there are an equal number of science and fine arts credits, y = z y − z = 0 Now, we are provided that the number of mathematics credits is twice the sum of science and fine arts credits, which can be represented in the form of equation as, w = 2 ( y + z ) 2 y + 2 z − w = 0 From the information provided we know that Liberal Arts credits exceed the mathematics credits by one third the number of Fine arts credits. This can be written in the form of equation as, x − w = 1 3 z x − 1 3 z − w = 0 The augmented matrix for the obtained equations is: [ 1 1 1 1 124 0 1 − 1 0 0 0 2 2 − 1 0 1 0 − 1 / 3 − 1 0 ] Apply Gauss Jordan reduction method to get the solution of the given system of equation. Begin by clearing the fraction in the rows of the matrix by the operation R 4 → 3 R 4 [ 1 1 1 1 124 0 1 − 1 0 0 0 2 2 − 1 0 1 0 − 1 / 3 − 1 0 ] → [ 1 1 1 1 124 0 1 − 1 0 0 0 2 2 − 1 0 3 0 − 1 − 3 0 ] Now, pivot the first nonzero element of first row and clear its column Perform the operation R 4 → R 4 − 3 R 1 , [ 1 1 1 1 124 0 1 − 1 0 0 0 2 2 − 1 0 3 0 − 1 − 3 0 ] → [ 1 1 1 1 124 0 1 − 1 0 0 0 2 2 − 1 0 0 − 3 − 4 − 6 − 372 ] Now, pivot the first nonzero element of second row and clear its column Perform the operation R 3 → R 3 − 2 R 2 , R 4 → R 4 + 3 R 2 , [ 1 1 1 1 124 0 1 − 1 0 0 0 2 2 − 1 0 0 − 3 − 4 − 6 − 372 ] → [ 1 1 1 1 124 0 1 − 1 0 0 0 0 4 − 1 0 0 0 − 7 − 6 − 372 ] Further perform the operation R 1 → R 1 − R 2 [ 1 1 1 1 124 0 1 − 1 0 0 0 0 4 − 1 0 0 0 − 7 − 6 − 372 ] → [ 1 0 2 1 124 0 1 − 1 0 0 0 0 4 − 1 0 0 0 − 7 − 6 − 372 ] Now, select the first nonzero element of third row and clear its column

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

7th Edition

ISBN: 9781337291484

Author: Waner

Publisher: Cengage

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Chapter 4, Problem 41RE

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To calculate: The combination of possible credits in each subject for Billy-Sean if candidates must select a total of 124 credits from the sciences, Fine arts, Liberal arts and Mathematics for the degree of Bachelor of Science.

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Chapter 4, Problem 40RE

Chapter 4, Problem 42RE

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Finite Mathematics and Application Calculus (Looseleaf) - Text Only

Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...

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The combination of possible credits in each subject for Billy-Sean if candidates must select a total of 124 credits from the sciences, Fine arts, Liberal arts and Mathematics for the degree of Bachelor of Science.

Solution Summary: The author calculates the combination of possible credits in each subject for Billy-Sean if candidates must select a total of 124 credits from the sciences, Fine arts, Liberal arts and Mathematics.

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To calculate: The combination of possible credits in each subject for Billy-Sean if candidates must select a total of 124 credits from the sciences, Fine arts, Liberal arts and Mathematics for the degree of Bachelor of Science.

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Chapter 4 Solutions