Please help me with the following question:

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kdh

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There is a pile of rice sacks. The weight of the three lightest sacks is 21% of the whole pile. The weight of four heaviest sacks is 3/5 of the whole pile. How many rice sacks are there in the pile?
 

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Hello. That exercise statement could be better worded, but let's see what we can do with it. Where they say, "of the whole pile", they mean the weight of the whole pile. Agree?

What have you thought about so far, kdh? Also, what class are you taking?

If you're expected to use algebra, then please show us what you've already tried -- so that tutors can see where you are in the process. Thank you!

EDIT: Not all of the individual rice sacks weigh the same, although some could.

:)
 
Last edited:
lev888 said:
Requires the knowledge of averages and some logic.
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Yes, both -- but more of the latter, I think.

I tried an approach that first expresses the two known group weights (i.e., those given as percents of the total weight) in terms of the remaining (middle) group's weight. I then wrote expressions for the average sack weight in each group.

I'm thinking those results show (by considering cases) that there's only one possible count for the number of sacks in the middle group such that those sacks' average weight falls between the average sack weights of the lightest and heaviest groups.

Let x = weight of lightest group
Let y = weight of middle group
Let z = weight of heaviest group
Let w = weight of entire pile

Hint: To start, use the given information to write a system of four equations, and then solve the system in terms of y.

?
 
I found a unique answer, by writing a pair of inequalities. The first step, of course, is to observe that the lightest 3 and the heaviest 4 can't overlap, so there must be a middle group of n-7 sacks. To keep things simple, I supposed the total weight is 100 (of some unit).
 
mmm4444bot said:

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...
www.freemathhelp.com

Can you share any thoughts?

Have you finished your last exercise? Good suggestions/comments there.

:)
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Thank you for the message. I have finished this exercise, but not the newest one I posted in the forum on the Math Olympiad problem.
 
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