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The Salary Solution

A man accepts a job for which he will be paid \$30.00 a day.Because this man has a history of calling in sick to work, hisemployer tells him that not only will he not get paid for these"sick days," but he will dock his pay \$15.00 for everyday that he cannot work.

1. If the man earns \$ 330.00, what is a possible combinationfor the number of days he worked and the number of days he wasout sick? Assume that he worked more than he was out sick.

2. What if he was out sick more than he worked? How many daysmust he have worked? How many did he call in sick?

3. How could you check this answer mathematically? Show andExplain how below.

The Soccer Situation

Super Middle School is starting a new after school intramuralprogram for soccer. Every Tuesday and Thursday any students whowant to can stay after to participate. The students are dividedinto teams and they play against each other. The goal is for allstudents to play the entire time. In order to assure that morestudents can play, the school has decided that teams can eitherconsists of the standard 11 players, or there can be a "shortformation" team that consists of a goalie, two strikers,three midfielders, and a sweeper. The school has 14 soccer fields.

Open the file "Soccer.xls."

Here you can see where I have begun a template that will assistyou with the following questions. You must decide what else needsto be done.

1. What is the largest number of students that can play soccerat the same time according to these guidelines? ______________What is the smallest?________

2. If 200 students show up for intramurals on Tuesday, howmany "standard" and how many "short formation"teams should be created so that all of the students can play atthe same time?

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3. Can you find a different solution to the question above?( Is their more than one way to divide the teams?) List all possibleways you could divide 200 students into teams. Which way wouldyou recommend the teams be divided and why?

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4. If 271 students show up Thursday, is it possible for allstudents to play at one time? If so, tell how many of each typeteam should be made. If not, tell how you could change the numberof players on each team so that 271 students could play at onetime.

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5. What is the largest number between 1 and 200 of kids thatcould not be divided into teams evenly among 14 fields? (Usingonly standard and short formation teams.) How do you know youranswer is correct?

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6. Think back to the problem with 200 students ( # 2 and #3).How could you design an "elimination tournament" forthe teams so that each team plays another team, and the winnermoves on to the next round, but the losers are eliminated fromthe tournament. This process must continue until there is onlyone team left. Which of the different team formations (from questionthree) would be easiest to do this with and why.

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Draw a diagram of the elimination tournament below.