**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...

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