**Educational Text: Solving Systems of Equations with Matrices****Problem Statement:**A farmer constructed a chicken coop using three different materials: chicken wire, wood, and plywood. The cost of the materials is as follows:- Chicken wire: $2 per square foot- Wood: $10 per square foot- Plywood: $5 per square footThe farmer spent a total of $47, and the total area covered by the materials was 11 square feet. Additionally, the farmer used 3 square feet more of chicken wire than plywood. We need to determine how much of each material the farmer used.**Questions:**1. How many square feet of chicken wire did the farmer use?2. How many square feet of wood did the farmer use?3. How many square feet of plywood did the farmer use?**Solution Approach:**To find the solution, we need to set up a system of equations based on the given information and solve it using the inverse of a matrix. Let's define:- $ x $: square feet of chicken wire- $ y $: square feet of wood- $ z $: square feet of plywood**Equations:**1. From the cost information:\[ 2x + 10y + 5z = 47 \]2. From the total area of materials:\[ x + y + z = 11 \]3. From the additional information about chicken wire:\[ x = z + 3 \]These equations can be solved using matrices for a clear solution.

Answered: Write a system of equations that…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

Find the augmented matrix for the following system of linear equations: -5x 16у + 4x 12y + + 97y -4 31x -31 || |||| | +
3) Our school's art teacher took his class to a concert hall and paid $512 for 10 adult tickets and 9 children tickets. The next day, our music teacher took our class to the same concert hall and paid a total of $831 for 17 children and 15 adults. If a represents the price of an adult ticket, and c represents the price of a child's ticket, which system of equations can be used to find how much each child ticket and each adult ticket cost? B) C) A) 19ac 512 32ac-831 10a+9c=512 15a+17c-83 10c+9=512 15c+17a-83 D) 19(a+c)=512 32(a+c) 83
The edges of a rectangular plece of plastic sheet are joined together to make a plastic tube. If the area of the plastic sheet is 284 cm", and the volume of the resulting tube is 134 cm³, what are the dimensions of the plastic sheet? Assume the sheet is longer than it is wide Determine the system of equations for this situation. Let x represent the width of the sheet, y represent the length of sheet. A represent the area of the sheet, and V represent the volume of the tube Assume that the width is used to form the circular base of the tube OA. A=xy v=mx² 4x OC. A-xy VaRx OB. A=xy v=Y²x² 4x OD. A=xy yx V=
On Monday, Sarah picked up lunches for her friends and spent $17.30 on 3 tofu banh mi and 2 bubble teas. On Friday she spent $26.75 on 5 tofu banh mi and 3 bubble teas. Set up a system of two linear equations to represent this situation, then write down the associated augmented matrix for this system. Do not solve this system.
Two teachers, Mrs. Dewsbury and Mrs. Pettit, decide to buy calculators and stickers for their classrooms. Mrs. Dewsbury buys 30 calculators and 50 pages of stickers for $95. Mrs. Pettit buys 40 calculators and 40 pages of stickers of each for $116. Write a system of equations to represent the cost of one calculator, c, and one page of stickers, p. A. c + p = 120 70c + 90p = 211 B. c + p = 211 30c + 50p = 40c + 40p C. 30c + 50p = 95 40cp = 116 D. 30c + 50p = 95 40c + 40p = 116
A small software corporation borrowed $315,000 to expand its software line. The corporation borrowed some of the money at 3%, some at 4%, and some at 5%. Use a system of equations to determine how much was borrowed at each rate when the annual interest was $13,500 and the amount borrowed at 4% was 22/12/2012 times the amount borrowed at 3%. Solve the system using matrices. amount borrowed at 3% $ amount borrowed at 4% $ amount borrowed at 5% $
An apartment complex has 1-bedroom apartments and 2-bedroom apartments. There are a total of 78 apartments in the complex, and there are twice as many 2-bedroom apartments as 1-bedroom apartments. If you want to find the number of apartments of each type, which system of equations could be used to solve the problem? Let x be the number of 1-bedroom apartments, and let y be the number of 2-bedroom apartments. A. x + y = 78 2 + y = x B. x + y = 78 2x = y C. x + y = 78 2y = x D. x + 2y = 78 2y = x E. x + 2y = 78 2x = y
A Sillall software corporation borrowed $115,000 to expand its software line. The corporation borrowed some of the money at 3%, some at 4%, and some at 5%. Use a system of equations to determine how much was borrowed at each rate when the annual interest was $5,300 and the amount borrowed at 4% was times the amount borrowed at 3%. Solve the system using matrices. amount borrowed at 3% amount borrowed at 4% $ amount borrowed at 5% Need Help? Master It Read It Submit Answer
A small software corporation borrowed $292,500 to expand its software line. Some of the money was borrowed at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was borrowed at each rate if the annual interest was $29,900 and the amount borrowed at 10% was 22 times the amount borrowed at 9%. Solve the system using matrices. Step 1 Let the amount borrowed at 9% be x, the amount borrowed at 10% be y, and the amount borrowed at 12% be z. The total amount borrowed was $292,500. The total annual interest was $29,900. The amount borrowed at 10% was 2- times the amount borrowed at 9%. Write a set of equations using the information given. Convert the percentage to decimal fraction. x + y + z = 292,500 .09 x +.10 y + |.12 V z = 29,900 X x - y = 0 Write the associated augmented matrix for the given system of equations. Recall that since there are three equations in the system, the matrix will have three rows. Use the coefficients of x, y and z as entries of the…
A “piggy” bank contains nickels, dimes and quarters totaling $6.20 in value. The bank contains 53 coins, and there are two more nickels than dimes. How many coins of each variety are there in the bank? Set up and solve a system of equations for this problem. Show all your work, and clearly indicate your answer!

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS