Math Is Fun Forum

Steven_157

Member

Registered: 2006-05-23

Posts: 1

Percentage problems

I work in school and am having trouble working out some percentages.  I have 203 hours that are split between a number of teachers throughout school.  One of the teachers is leaving so another 20 hours are available.  I then have some children leaving for secondary school so 51.5 hours will be lost.  I know that the equation to work out the percentage of hours that each teacher will be losing is 230+20/51.5 which comes to around 23%, however a number of my colleagues think that the equation should be 203/51.5-20 and I cannot explain to them why they are wrong?  Can u help?

Any help would be much appreciated,

Thanks,

Julie Elliott

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Percentage problems

I assume there are now only nine teachers and therefore (203 - 51.5)/9 = time each can work.
So the percent drop is 17% because
the ten teachers used to work 20.3 hours each, but now the nine
workers can work (203-51.5)/9 hours each.  16.83333hrs

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igloo myrtilles fourmis

Pi Man

Guest

Re: Percentage problems

The number of total hours worked used to be 203.   Now it's 171.5 (203 + 20 - 51.5).   Assuming the original number of teachers was X, they each used to work 203 / X hours.   With the changes both in the numbers of hours and teachers, they now work 171.5 / (X-1) hours.   So the change in the number of hours each teacher works is:  (203 / x) - (171.5 / (X-1)). Divide that by the the original number of hours they worked (203 / x), and you have your percentage.   So the percentage of hours they lose can not be computed without knowing the number of teachers.   Which makes perfect sense.   If you were one of 2 teachers and the other quit, your workload would increase 100%.    If one out of 100 teachers quit, your increase in workload is much smaller.   

If you wanted to know the percentage of hours lost by all teachers collectively rather than by each teacher, the formula would be (203 - 171.5) / 203.   That's roughly 15.5%.

atulvek

Member

Registered: 2006-04-21

Posts: 5

Re: Percentage problems

goodone

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Atul Vek