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## #1 2005-12-06 05:37:06

Bobba_Jim
Member
Registered: 2005-12-06
Posts: 2

### Help with percentages

Hi All,

I have a mathematical problemt hat I just can't work out so I figured I'd put out there and see if anyone can help. I need a formula for the following situation:
---
Bob works 7 hours a day dealing with completed questionnaires posted to him.
Most questionnaires are easy to deal with and take him 10 minutes to deal with.
But if a questionnaire needs special attention it takes Bob 30 minutes to deal with it.

Assuming that only 20% of questionnaires need special attention, how many questionnaires can Bob deal with on 1 day?
---

My brain cannot deal with this problem, but I'm hoping I have provided all the neccessary information for a solution. Never was any good with percentages.

Hope someone has fun working it out or can point me in the right direction!

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## #2 2005-12-06 06:23:10

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Help with percentages

We need to work out the average time that Bob would take to deal with a questionnaire.

80% of them are short and he takes 10 minutes, so we do 80%/100% * 10 minutes = 8 minutes.
The other 20% are long and take 30 minutes, so we do 20%/100% * 30 minutes = 6 minutes.

Add these to get the total average time and we get 14 minutes.

He works for 7 hours, which is 420 minutes.

Therefore, he can deal with 420/14 = 30 questionnaires in 1 day.

Why did the vector cross the road?
It wanted to be normal.

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## #3 2005-12-06 10:23:44

MathsIsFun
Registered: 2005-01-21
Posts: 7,659

### Re: Help with percentages

And backwards:

He has 30 questionnaires. 24 (ie 80%) take 10 mins, and 6 (ie 20%) take 30 mins. 24×10 + 6×30 = 420 mins = 7 hrs.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #4 2005-12-06 10:52:29

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: Help with percentages

I will come late on this one also.  Different strokes for different folks.  I like to do these types of things algebraically.

7 hours = 420 minutes

special questionaires = .2 q  (q=any questionaire)

simple questionaires = .8 q

total time = .8q(10 minutes) + .2q(30 minutes)

420 = .8q(10) + .2q(30)

420 = q(8 + 6)

q = 420/14 = 30

The average concept used by mathsyperson never even occured to me.  Go figure.

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## #5 2005-12-06 11:47:17

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Help with percentages

It's pretty much the same method though, I was just explaining it in a simpler way.

Why did the vector cross the road?
It wanted to be normal.

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## #6 2005-12-07 00:10:34

Bobba_Jim
Member
Registered: 2005-12-06
Posts: 2

### Re: Help with percentages

Thank you guys that's so helpful, I'd been struggling with that one! Seems so simple once you know the answer

Thanks again for the time you've all spent helping me out.

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