Clean Your Room

Each day Chris is chided for not cleaning up his room, so he picks up approximately 10 percent of the items on the floor in the morning. (He always rounds off to the nearest whole number if his calculations result in fraction.) Each day, ten new items somehow end up on the floor. If he has a clean floor on Sunday morning, how many items will be on the floor on Saturday night?
Source: NCTM Mathematics Teacher, October 2006

Solution
Sunday morning starts with a clean floor but in the night 10 items appear.
Monday he cleans up 10\% but ends up with 10-(.1)10+10=19.
Tuesday 19-(.1)19+10=19-2+10=27
Wednesday 27-(.1)27+10=27-3+10=34
Thursday 34-(.1)34+10=34-3+10=41
Friday 41-(.1)41+10=41-4+10=47
Saturday 47-(.1)47+10=47-5+10=52

Answer: 52

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About mvtrinh

Retired high school math teacher.
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