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

4th Edition

ISBN: 2818000007824

Author: Stewart

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 11.1, Problem 70E

To determine

To find:

The number of milliliters required of three acid solutions.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.1, Problem 69E

Chapter 11.1, Problem 71E

Students have asked these similar questions

Solve for the matrix X: X (2 7³) x + ( 2 ) - (112) 6 14 8

5. Solve for the matrix X. (Hint: we can solve AX -1 = B whenever A is invertible) 2 3 0 Χ 2 = 3 1

Write p(x) = 6+11x+6x² as a linear combination of ƒ (x) = 2+x+4x² and g(x) = 1−x+3x² and h(x)=3+2x+5x²

Chapter 11 Solutions

ALGEBRA AND TRIGONOMETRY-WEBASSIGN

Ch. 11.1 - If a system of linear equations has infinitely...Ch. 11.1 - Write the augmented matrix of the following system...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - 5-10 Dimension of a Matrix State the dimension of...Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

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.

Concept explainers

Videos

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

Want to see the full answer?

Chapter 11 Solutions

To find:

The number of milliliters required of three acid solutions.