Explanation Given Information: The number of apples and oranges collectively is equal to the number of bananas in each basket. Cost of each apple, banana and orange is $ 0.85 , $ 0.20 and $ 0.76 respectively and each basket should have 18 pieces of fruit and its making costs $ 9 . Formula used: The following elementary row operations may be performed on an augmented matrix to get reduced row echelon form: Step1:Swap any two rows if required. Step2:Multiply the row by the desired non-zero number. Step3:Now, add multiples of another row beneath or above it to change the row being operated. Gauss-Jorden elimination method is used to convert the system of linear equations into diagonal form by using the above three row operations repeatedly. Calculation: Suppose x be the number of apples, y be the number of bananas and z be the number of oranges in a basket. Consider that each basket has 18 pieces of fruit. So, the equation becomes, x + y + z = 18 Also consider that the grocery store makes a fruit basket for $ 9 and charges $ 0.85 for an apple, $ 0.20 for a banana and $ 0.76 for orange, This gives the equation, 0.85 x + 0.20 y + 0.76 z = 9 Also consider that number of apples and oranges is equal to the number of bananas. This gives the equation, x + z = y Thus, the system of equations formed is { x + y + z = 18 0.85 x + 0.20 y + 0.76 z = 9 − x + y − z = 0 . The augmented matrix formed from the system of linear equations is [ 1 1 1 18 0.85 0.20 0.76 9 − 1 1 − 1 0 ] Pivot the matrix about the boxed element as follows: Transform 0.85 into 0 by multiplying row 1 by − 0.85 and adding the result to row 2 . Transform − 1 into 0 by multiplying row 1 by 1 and adding the result to row 3 . [ 1 1 1 18 0.85 0.20 0.76 9 − 1 1 − 1 0 ] → R 2 + ( − 0.85 ) R 1 R 3 + ( 1 ) R 1 [ 1 1 1 18 0 − 0.65 − 0.09 − 6.3 0 2 0 18 ] Transform 0.65 into 1 by multiplying row 2 by − 1 0.65 : [ 1 1 1 18 0 − 0.65 − 0.09 − 6.3 0 2 0 18 ] → ( − 1 0.65 ) R 2 [ 1 1 1 18 0 1 0

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 2, Problem 23RE

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To calculate: The number of apples, bananas and oranges in each basket if each basket should have 18 pieces of fruit and its making costs $9 such that the cost of each apple, banana and orange is $0.85, $0.20 and $0.76 respectively. The number of apples and oranges collectively is equal to the number of bananas in each basket.

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Chapter 2, Problem 22RE

Chapter 2, Problem 24RE

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Chapter 2 Solutions

Finite Mathematics & Its Applications (12th Edition)

Ch. 2.1 - 1. Determine whether the following systems of...Ch. 2.1 - Give the meaning of each of the following...Ch. 2.1 - 3. Perform the indicated elementary row...Ch. 2.1 - State the next elementary row operation that...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - Prob. 2E Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 18, perform the indicated elementary...Ch. 2.1 - In Exercises 18, perform the indicated elementary...

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Solution Summary: The author explains how Gauss-Jorden elimination method is used to convert the system of linear equations into diagonal form.

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