MAT 117 - SPRING C 2022 NAME: UNIT A PROBLEM SET (1 pt) Directions: Complete the problems on this sheet. If you do not have a printer, complete the problems NEATLY on a separate sheet of paper. Show all work and include appropriate units where applicable. Box all final answers. 1. Solve the following equations for X. Leave your answers as integers or fractions in lowest terms (do not round any answers). a. [3 pts] 3(9x + 2) + 21x = (6x -8)+75x b. [3 pts] V3x - 5 - 3=8 2. Miss Kito and Mr. Fishman played 81 games of their favorite 2-player game, 7 Wonders Duel. Miss Kito ultimately won 9 more games than Mr. Fish did. How many games did they each win? . [3 points] Define variables to represent the unknowns and setup the necessary equations to answer the question. X = # of games won by fishman y = # of games won by kito Total number gomes Played = $1 .... Xty = 81 kito had a total of 9 more wins than Fishman . Y= X+ 9 b. [3 points] Algebraically solve the equation you created and express your final answer using a complete sentence and appropriate units. (You will not receive full credit if a trial and error method is used in place of an algebraic method.)3. Miss Kito's grandfather passed away and she attended the reading of the will. The estate was valued at $4,567,890. It was decided that - of the estate would be given to his children. Of the remainder, - would be 1 used to create a scholarship for mathematics majors at Fishtopia University and the rest would be divided evenly among his three grandchildren, of which Miss Kito was one. a. [3 points] How much money was used for the scholarship? b. [3 points] What fraction of the estate did Miss Kito end up inheriting? 4. There are 100 seniors in Fishtopia High School. Each senior has their own locker numbered #1-100 down a long corridor. As a graduation tradition, all the seniors line up and walk one at a time down the hallway. The first senior changes all the locker positions (so, the first person in line opens all the locker doors). The second senior then changes the position of every other locker (so, since all the lockers are now open, she closes door #2, closes door #4 etc. while not touching door #1 or door #3, etc.). The third senior then changes the position of every third locker (so, he closes door #3, opens door #6, etc.). This continues until all seniors have had an opportunity to walk down the corridor, only changing the position of the locker doors that correspond with multiples of their position in line (so, the last senior only changes the position of locker #100, while not touching any of the other lockers). [Note: Changing the position of a locker means opening it if it is closed or closing it if it is open.] [3 points] How many students touched locker #12? Is this locker open or closed at the very end after all 100 seniors have walked down the corridor? b. [3 points] At the very end, only ten of the lockers will be open. Which lockers will be open at the very end? What do these lockers have in common