Multiple percentage problem where values rely on other values

AKR05

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Hi!

I was hoping to get some help with a percentage problem on some tests for job applications! I can't find any similar examples online which is annoying as I don't think its that complicated but I can't work it out :(

It is help with a style of questions which asks to find the percentages and put them into a pie chart. The issue is that some of the percentages rely on the other values. Here is the example I couldn't do:

If 20 reports were filed this week by different people, work out the percentage completed by each person:

Andrew - Submits 5 reports this week
Barbara - no information given
Charles - Submits two thirds (2/3) less reports than Barbara
Jane - reports five less reports than Charles

I tried using simultaneous equations to find what amount of the twenty each person had submitted but I couldn't get it right. If anyone could solve this or give some tips on how to solve similar problems it would be very much appreciated!

Also, this is my first post so if it is in the wrong category please let me know which one it should be in, thanks!

Many thanks in advance,
Alice
 
Can you post your equations and solution?
One equation should be enough, though. Barbara submits x, the other 2 can be expressed through x.
 
One thing that may be tricky is the part, "two thirds (2/3) less reports than Barbara". If one number is 2/3 less than another, what does that mean? I'd take it to mean x - 2/3 x, which is 1/3 x. That is, Charles submits 1/3 as many as Barbara.
 
Hi!

I was hoping to get some help with a percentage problem on some tests for job applications! I can't find any similar examples online which is annoying as I don't think its that complicated but I can't work it out :(

It is help with a style of questions which asks to find the percentages and put them into a pie chart. The issue is that some of the percentages rely on the other values. Here is the example I couldn't do:

If 20 reports were filed this week by different people, work out the percentage completed by each person:

Andrew - Submits 5 reports this week
Barbara - no information given
Charles - Submits two thirds (2/3) less reports than Barbara
Jane - reports five less reports than Charles
Problems where "values depend on other values" are called "algebra"!

Since we are not told how many reports Barbara submits, call that "B". Charles submits "two thirds less", B- (2/3)B= B/3, reports and James submits B/3- 5. Finally Andrew submits 5 reports.

All together they submit 5+ B+B/3+ B/3- 5= 5B/3= 20 reports. Solve for B.

Oh, dear! I have a problem with this! From 5B/3= 20, we get B= 12. Then Charles submits 12/3= 4 reports and James submits 4- 5= -1 report! How can one submit "-1" reports? (I have read some reports that might fit that category!)

I tried using "2/3 of" rather than "2/3 less" but that results is fractional answers.

I tried using simultaneous equations to find what amount of the twenty each person had submitted but I couldn't get it right. If anyone could solve this or give some tips on how to solve similar problems it would be very much appreciated!

Also, this is my first post so if it is in the wrong category please let me know which one it should be in, thanks!

Many thanks in advance,
Alice
 
Last edited:
Oh yuck.
Why can't math teachers get their terminology right? Much of the confusion in this problem could have been skipped if the teacher had only clarified what s/he meant. I don't understand why anyone wouldn't clarify what they meant with one word!

Pet peeve over.
 
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