Willowside POW # 4: Justin Needs Out!

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Justin sat in the back of Mr. Bott’s math class. He did not belong in the back of this room, in Mr. Bott’s class or even at Willowside Middle School. He was frustrated with this new school, with the kids and especially, with Mr. Bott.
Back at his old school in New York City, Justin had been known as a class star: great at math, soccer, art and even at singing. In fact, he had been key in helping the school form a choir with the music teacher. He was considering running for class president and was sure that he would win. He loved his school, his friends and the sense of control over his destiny. It all got messed up when his parents decided to move out to Willowside. Now he was far away from civilization, in the middle of nothing other than fruit trees and miles and miles of weeds. He knew he was no longer in NYC. when he came to school in a sports coat, like he did in his previous school, to the stares and snickers of the other kids. Thanks to a tip from Tyrone, the only kid who dared speak to him, he quickly stashed the coat into his locker and tried to fit in. Then he was told by the school secretary that he was to be placed into Mr. Bott’s math class because there was room for him there.
“But Mrs. Guzmán, Mr. Bott’s class is the remedial one. I was in advanced math in my other school: they sent the records. I don’t belong with those kids.” he said, pointing across the courtyard to Mr. Bott’s door. He saw Tyrone there and felt a little pang of guilt: he had not meant to include Tyrone with the “those kids” label.
“I know, dear. Your school hasn’t sent over the records yet and maybe it is for the best that you are not quite so challenged. After all, you are new here, you know?”
“Duh!” thought Justin to himself. Mrs. Guzmán turned at her desk, grabbed a sheet of paper and handed it to Justin. It was his class schedule. She had printed his name at the top and laminated it. “If this was a temporary schedule, why did she go through all the trouble make it look so permanent?” Justin took the schedule and walked across the courtyard. He got to the door just as Mr. Bott was closing it. The little window in the door was covered by black construction paper. Mr. Bott looked at him cautiously.
“You are new here.” Justin wondered why all the adults in Willowside felt the need to state the obvious. “Don’t tell me they assigned you to my class.” Mr. Bott looked visibly angry. “But I already have five kids over the standard student load.” He looked up to the sky in exasperation. Justin could think of a few choice words he would say in response to Mr. Bott’s rant, but he chose to stay quiet. It wasn’t like he wanted to be there either. 
“Well, come on, class is starting and you ARE late.” Justin moved past Mr. Bott and into the intense focus of all the kids. They were all sitting in rows of individual student desks. There were six rows, each with six desks. There was next to nothing on the wall. A few faded posters hung limply along the back of the room. No windows except for the covered up on on the door. In the front was an old chalkboard. Justin had only seen a real chalkboard in the movies. His L.A. school had either whiteboards or Smartboards. 
“Class, this is a new student to our class.” He turned to Justin. “What’s your name, by the way?” Justin told him, but Mr. Bott was rummaging through his desk drawer and pulled out a textbook. “Here is your math book, Jason.”
“Sir, my name is Justin”
“Yes, sorry, Justin.” Justin saw a line of spittle collect along the edges of Mr. Bott’s mouth. The spittle jumped up and down as Mr. Bott spoke.  
“Let’s see if you guys can impress me. Here is the math problem for the day.” Mr. Bott wrote the following problem on the chalkboard:  
  "On the first day, I will pay you $1,000 early in the morning. At the end of the day, you must pay me a commission of $100. At the end of the day, we will both determine your next day's salary and my commission. I will double what you have at the end of the day, but you must double the amount that you pay me. Will you work for me for a month?"
Justin realized then that he could get out of this class if he could just manage to “impress” Mr. Bott. 

Your Task: Work this problem out for Justin and impress Mr. Bott with your mathematical and logical insight.

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