As part of a crazy game of CharDeeMacDennis, Dennis and Charlie enter into a high stakes beer drinking contest for Round 6. The total number of 12 oz beer bottles drunk by the two is 50. The number of beer bottles drunk by Charlie exceeds thrice the number of beer bottles drunk by Dennis by 6. The goal in this Problem is to find the number of beer bottles drunk by each of them. You are not just evaluated on being able to solve the Problem but actually on being able to find the inverse of a square matrix and use it to solve a system of linear equations. So please follow the steps below and use the requested method. Magically coming up with the solution or using another method to find the solution will get you no credit. a. What are the unknowns (variables) in this problem ? Pick a letter for each unknown (x, y, z, etc.) and clearly write what it is. b. Write down all the linear equations that we can write based on the available information. Give your final answer as a properly written system of linear equations. c. Write the corresponding augmented matrix. DO NOT SOLVE THE SYSTEM OR REDUCE THE MATRIX YET.
Problem 5:
As part of a crazy game of CharDeeMacDennis, Dennis and Charlie enter into a high stakes beer drinking contest for Round 6. The total number of 12 oz beer bottles drunk by the two is 50. The number of beer bottles drunk by Charlie exceeds thrice the number of beer bottles drunk by Dennis by 6.
The goal in this Problem is to find the number of beer bottles drunk by each of them.
You are not just evaluated on being able to solve the Problem but actually on being able to find the inverse of a square matrix and use it to solve a system of linear equations.
So please follow the steps below and use the requested method. Magically coming up with the solution or using another method to find the solution will get you no credit.
a. What are the unknowns (variables) in this problem ?
Pick a letter for each unknown (x, y, z, etc.) and clearly write what it is.
b. Write down all the linear equations that we can write based on the available information.
Give your final answer as a properly written system of linear equations.
c. Write the corresponding augmented matrix.
DO NOT SOLVE THE SYSTEM OR REDUCE THE MATRIX YET.
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