Diem has just completed a series of job interviews with several institutions. She received three good offers from those interviews. Unfortunately, she only has a few more hours to decide which one to take. She is completely exhausted and cannot make up her mind. Luckily, she has discussed all the job offers with her trustworthy friend, Mark, last night. Mark promised her to run a comparison between the offers based on projected salaries and future opportunities. The plan was for him to send her the result in the morning. Diem decides to take the job offer given by the institution that Mark's analysis would suggest. The next morning, she opens her email to look for Mark's respond. There are only two emails from Mark that morning. The first one is simply a block of numbers: 5 -27 -17 -15 -13 -16 7 0 6 -20 -27 -22 -12 -25 14 5 6 -13 1 7 -13 0 -1 2 14 -24 -19 -6 -25 -20 7 7 Diem immediately recognizes that this is a coded message. Mark is using his work email account and for many reasons their conversation must stay private. She knows Mark uses O for space and the rest of the integers in the range -13 to 13 for the alphabet. (I.e., -13 = A, -12 = B, ..., 12 = Y, 13 = Z) All she needs now is the translator which changes with every coded message. She checks her email account again and finds the second message from Mark. It reads: A family has four children, two girls and two boys in that order. The sum of their ages without the youngest one is 30, and without the oldest one is 22. The oldest daughter is 12. The sum of their ages without the oldest son is 26. Can you find their ages from the oldest to the youngest? Sometimes the statement of a problem is more important than its solution, don't you agree? Good luck and congratulations." After reading the second email, Diem gets excited. She gathers her pen, paper and calculator. First, she translates the word problem into a system of linear equations. She pays close attention to the order of each sentence. She rewrites the equations in the matrix form carefully. Then, she does a simple matrix multiplication on her calculator. (She can do this by hand, but she is too tired.) The result doesn't make any sense to her. She makes a table, listing the alphabets versus their assigned numbers. Suddenly, she remembers that she needs to decode the coded message. She runs a few simple operations on her calculator and she smiles. (She would do all the calculations by hand if she had more time.) She translates the numbers to letters and verifies her work. Finally feeling relieved, she shoots an email to Mark saying, Got it, thanks for your help. She sends out the replies to her job offers and takes the rest of the day off. What does Diem get by translating Mark's second email into a system of linear equations? Determine the message in Mark's first email to Diem. Name at least one institution or company that offered her a job. Which job does Diem take? What was the offer? Diem has just completed a series of job interviews with several institutions. She received three good offers from those interviews. Unfortunately, she only has a few more hours to decide which one to take. She is completely exhausted and cannot make up her mind. Luckily, she has discussed all the job offers with her trustworthy friend, Mark, last night. Mark promised her to run a comparison between the offers based on projected salaries and future opportunities. The plan was for him to send her the result in the morning. Diem decides to take the job offer given by the institution that Mark's analysis would suggest. The next morning, she opens her email to look for Mark's respond. There are only two emails from Mark that morning. The first one is simply a block of numbers: 5 -27 -17 -15 -13 -16 7 0 6 -20 -27 -22 -12 -25 14 5 6 -13 1 7 -13 0 -1 2 14 -24 -19 -6 -25 -20 7 7 Diem immediately recognizes that this is a coded message. Mark is using his work email account and for many reasons their conversation must stay private. She knows Mark uses O for space and the rest of the integers in the range -13 to 13 for the alphabet. (I.e., -13 = A, -12 = B, ..., 12 = Y, 13 = Z) All she needs now is the translator which changes with every coded message. She checks her email account again and finds the second message from Mark. It reads: A family has four children, two girls and two boys in that order. The sum of their ages without the youngest one is 30, and without the oldest one is 22. The oldest daughter is 12. The sum of their ages without the oldest son is 26. Can you find their ages from the oldest to the youngest? Sometimes the statement of a problem is more important than its solution, don't you agree? Good luck and congratulations." After reading the second email, Diem gets excited. She gathers her pen, paper and calculator. First, she translates the word problem into a system of linear equations. She pays close attention to the order of each sentence. She rewrites the equations in the matrix form carefully. Then, she does a simple matrix multiplication on her calculator. (She can do this by hand, but she is too tired.) The result doesn't make any sense to her. She makes a table, listing the alphabets versus their assigned numbers. Suddenly, she remembers that she needs to decode the coded message. She runs a few simple operations on her calculator and she smiles. (She would do all the calculations by hand if she had more time.) She translates the numbers to letters and verifies her work. Finally feeling relieved, she shoots an email to Mark saying, Got it, thanks for your help. She sends out the replies to her job offers and takes the rest of the day off. What does Diem get by translating Mark's second email into a system of linear equations? Determine the message in Mark's first email to Diem. Name at least one institution or company that offered her a job. Which job does Diem take? What was the offer