The title of this P.O.W. is Justin Needs Out! In this problem you are working for someone, and you get paid $1,000 on the first day, but have to pay a commission of $100. The next day your salary is double what you had at the end of the day, and the commission is double what it was the day before. You need to figure out if you will work for a month. The important information is the amount of salary you get each day and the amount of commission you pay each day. The main math topics in this problem are ratios (salary to commission) and patterns and trends.
To solve this P.O.W. I made a table with five columns, one for the day, one for the salary, one for the commission, one for the profit, and one for the fraction of the salary the commission is. I filled out the columns for day one through fourteen and saw and pattern in the fractions column. It started with one tenth, and then the denominator decreased by one every column. I filled that column in using the pattern. I knew to try this strategy because I have solved problems similar to this, using tables, and it is a great way to organize data. I ran into many problems solving this problem. I asked my dad to check my work after making a table, and three times it turned out I had to start over again because I didn’t read the problem carefully enough. The only resources I used was my dad to check my work and tell me when I’ve totally screwed up (because I have a habit of doing that) and a calculator to save time adding and multiplying large numbers.
No, if I was given this offer I would not except, because the commission doubles every day, but the salary decreases first, and then is doubled every day. Infact, by day twelve I would have given back all the money I earned from day one!By the end of the month I would have lost much, much more money than I had earned. I know my solution is correct because if the salary decreases then doubles, and the commission doubles with out decreasing, eventually you have to be paying more then your receiving. There are no other possible answers.
This problem was interesting because I could solve it using a pattern and I didn’t have to do the math all the way up to the thirtieth day. This problem challenged me because I wasn’t sure what to put in the fractions column after one over one. It stumped me for a while until I asked for help from my dad, and he explained that one over zero would be infinity, and after that I could just go into negative numbers. This problem reminded me of a problem we did in fourth grade where their was one person working for fifty dollars a week and another who started out with one penny a day but the salary doubled every day. Then you had to figure out who would have more money after certain amounts of time. I didn’t manage my time very well this week. I started solving the P.O.W. on Wednesday, finished it on Saturday, started the write up on Saturday and finished it on Sunday. Next week I want to manage my time better by using the P.O.W. time management sheet.