Explanation Given: A chemist has three acid solutions at various concentrations. The first is 10% acid, the second is 20%, and the third is 40. If the chemist has to use four times as much of the 10% solution as the 40% solution Approach: Let x , y , and z represents the amount of 10%, 20%, and 40% solution. Write the augmented matrix of the system. Use elementary row operations to change the augmented matrix to row-echelon form. Write the new system of equations that corresponds to the row-echelon form of the augmented matrix and solve by back-substitution. Calculation: The chemist used 18% of each solution to make 100 ml. 10 % x + 20 % y + 40 % z = 100 ml of 18 % 10 x + 20 y + 40 z = 1800 Since the total amount of the solution is 100 ml. Thus, x + y + z = 100 The chemist uses four times as much of the 10% solution as the 40% solution. Mathematically, x − 4 z = 0 The system of equations is given by, 10 x + 20 y + 40 z = 1800 x + y + z = 100 x − 4 z = 0 Consider the system of equations { 10 x + 20 y + 40 z = 1800 x + y + z = 100 x − 4 z = 0 . The augmented matrix is given by, [ 10 20 40 1800 1 1 1 100 1 0 − 4 0 ] Transform the augmented matrix into row echelon form. Perform the transformation R 1 → R 1 10 . [ 10 10 20 10 40 10 1800 10 1 1 1 100 1 0 − 4 0 ] → [ 1 2 4 180 1 1 1 100 1 0 − 4 0 ] Perform the transformation R 2 → R 2 − R 1 . [ 1 2 4 180 1 − 1 1 − 2 1 − 4 100 − 180 1 0 − 4 0 ] → [ 1 2 4 180 0 − 1 − 3 − 80 1 0 − 4 0 ] Perform the transformation R 3 → R 3 − R 1 . [ 1 2 4 180 0 − 1 − 3 − 80 1 − 1 0 − 2 − 4 − 4 0 − 180 ] → [ 1 2 4 180 0 − 1 − 3 − 80 0 0 − 8 − 180 ] Perform the transformation R 2 → − R 2

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ISBN: 2818000007824

Author: Stewart

Publisher: CENGAGE L

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Chapter 11.1, Problem 70E

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The number of milliliters required of three acid solutions.

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Chapter 11.1, Problem 69E

Chapter 11.1, Problem 71E

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The number of milliliters required of three acid solutions.

Solution Summary: The author explains that a chemist has three acid solutions at various concentrations, and uses four times as much of the 10% solution as the 40% solution.

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To find: The number of milliliters required of three acid solutions.

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To find:

The number of milliliters required of three acid solutions.