Open Middle®
Directions: What is the fewest number of people surveyed if exactly 93.6% of people completed a survey?
Hint
How could we determine if only one person could have completed it? Can we have partial people complete the survey?
Answer
93.6% of people would be 93.6 people out of 100. Since it is not possible to have .6 people, then it could be 936/1000 with 1000 being the number of people surveyed. Unfortunately 1000 is not the fewest number of people that could be surveyed. Reducing 936/1000 we get 117/125 and 125 people is the fewest number of people that could have been surveyed.
Source: Robert Kaplinsky
The answer is 47 if the percentage was rounded to the nearest 0.1%. Since percentages are often rounded, it would be better to write “exactly 93.6%”.
Good point Daniel. I will make the change.
I started off with the following: What is the fewest number of people surveyed if exactly ___% of people completed a survey?
With some mild help, students started replacing the ___ with friendly percentages like 50 and then some not-so-friendly percentages like 57. Small group and then class discussions were had. This gave them an idea of HOW this can be done if the percentage was known. Once they got to 93.6%, it was a piece of cake. Thanks, Robert!
Awesome! Thanks for sharing your experience Andrew.
A typo in the title: Interpreting is spelled with only one t.
Thanks! Fixed it. =)
Wondering if you might want to add the Common Core Standard tag (6.RP.3?) on this one…
Nice catch Cee. For some reason no standards were listed on this problem. Not sure why. Fixed now.
How did you get 117/125?
What do you get when you solve it?
Do your students guess and check or do they simplify 936/1000?
I did not realize the depth of this problem until I did it in class.
Easier to work on the 6.4% who fid not complete the survey. 64/1000 simplifies to 8/125
ok this makes sense