Sell the wheat!

Algebra Level 2

Mifty is a farmer who wants to sell the wheat cultivated in her farm. One day, a customer comes to her house and gives her 3 barrels having capacities to store 5 kg, 15 kg, and 25 kg of wheat, respectively. The customer puts a condition before her. She will have to sell him exactly 49 kg of wheat by using only these 3 barrels for measurement. What is the minimum number of moves she will require if she has unlimited supply of wheat?

Dividing a barrel is not allowed. If she wants to use one barrel, then it should be filled completely. Help Mifty!

3 It's an impossible task 21 9

3 solutions

Swarali Patil
May 4, 2014

The problem needs application of one of the fundamental theories in algebra.
If you add or subtract multiples of a same number, then your answer will always be the multiple of that number.
So, even if you do infinitely many operations with these 3 barrels, giving the customer 49 kg wheat is just impossible.

yes you are right

sunshine 张 - 4 years, 7 months ago

Well. It depends. I can use the 25 along the 15 if we say that I can just pass this wheat to my client.

With the 5 kg one I fill in the 25 then I fill in another 10. Lastly i fill in the 15 top the max and if we agree that I somehow stored all this wheat I will only fill in the rest of 14 with 1 kg remaining in the 15 one. Other than that yeah it's not possible.

Alexandru Gheorghe - 4 years, 7 months ago

Thanks for your response :) But I didn't understand your solution, can you please explain it again?

Swarali Patil - 4 years, 5 months ago

So it's a trick question? This is silly

Peter Kluth - 4 years, 6 months ago

Well, I respect your personal opinion but I think questions can never be silly whereas answers can... Here, the answer totally makes sense to me. I am not trying to change your opinion, I just thought I should clear my point. Thanks for your response :)

Swarali Patil - 4 years, 5 months ago

Stuart McKenzie
Oct 17, 2016

Because the three barrels are 5kg, 15kg and 25kg then the maximum amount you can assemble using only these 3 barrels is (5+15+25=45) 45kg. Therefore it is impossible to gather 49kg using them no matter how many moves you make.

This explanation is wrong, barrels should be used for measurement only, not for storage.

Maxim Khenkin - 4 years, 7 months ago

I agree, Maxim.

Matt Smith - 4 years, 7 months ago

correct! :)

Swarali Patil - 4 years, 5 months ago

She should measure out 50kg .. a 25kg, a 15kg and two 5kg buckets .. and then take out a kg. And if she doesn't know what a kg of wheat looks like then she shouldn't be a farmer.

Steven Shoen - 4 years, 7 months ago

And you should not be a mathematician

Geraint Dawe - 4 years, 7 months ago

Haha, but the point I am trying to make here is about algebra, not farming. Thanks for your response :)

Swarali Patil - 4 years, 5 months ago

25+12+12 Fill 25, empty to 49 bucket Fill 15, from it fill 3, you ending up with 12 which empty to 49, so you have 37 there Repeat previous step Not really sure how many steps there

Alexander Petrov - 4 years, 4 months ago

Actually the buckets on my side of the planet all hold a certain volume such as liters.. not a certain mass such as kg.

Steven Shoen - 4 years, 7 months ago

Actually, you are right! There will be a negligible error since I cannot always control the density of those wheat grains. But again, I can write that problem in several ways using different terms. I just want readers to relate this concept from algebra with real life scenarios. Thanks for your response :)

Swarali Patil - 4 years, 5 months ago

negligible error? spoken like a person that has never measured the difference between wet and dry material. it can be several hundred percent.

Steven Shoen - 4 years, 3 months ago

I don't agree. Problem can be solved. You have to do many move. Since it is math and algebra so do like this (25*9+15+5)/5 so each bucket will give 49kg wheat

anoop Sihag - 4 years, 6 months ago

Mathematical it works but you assuming you can break it up into 5 equal piles. Your base unit is 5, the minimum you can move out of your 245kg pile is 5kg. All this would leave you with a 245kg of wheat as opposed to an infinite pile.

Chris Summers - 4 years, 5 months ago

George Melas
Jan 25, 2017

No combination yields 49

Sell the wheat!

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