Brainsteem Quickfire questions is a series of slightly easier, certainly faster, mathematical challenges in the Brainsteem family!
Winner will get 2 SBD or a @randowhale upvote for free!
Second prize is 1 SBD for free selected randomly from all other correct solutions!
Let's write the fraction 1/20 as the sum of two other unit fractions:
1/20 = 1/a + 1/b , such that a and b are positive integers and a < b.
Find the smallest possible sum (a+b).
Easy!
Prizes
To qualify you must upvote this post and write the answer in a comment.
To win First Prize you must include the answer and a valid method.
The First Prize will be 2 SBD or the chance of a @randowhale upvote.
The Second Prize will be 1 SBD to any other correct answer in the comments section, chosen at random.
Prizes will be awarded after the 7 days have expired. Winners will be announced at the next puzzle after the draw.
The main thing is to enjoy the challenge and maybe learn something new.
Come and check out other challenges currently live!
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Brainsteem #6 Prize Maths Puzzle [Win 2SBD+1SBD]
Brainsteem #5 Prize Maths Puzzle [Win 2SBD+1SBD]
And don't forget to upvote each other's comments to bring cheer to the whole community!
And never assume that previous answers posted are all necessarily correct :-)
This is again the sort of question where the solver needs a method to reduce the possible space of answers.
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The smallest possible sum (a+b)= 36+45=81
1/20= 1/a+1/b= (a+b)/ab --> 20(a+b)=ab
b=20a/(a-20)=20+400/(a-20)
Hence a+b=a+20-400/(a-20),
By differentiation, a+b is minimized when (a-20)^2=400, i.e. a=40, b=40.
However, this does not fit the requirement a<b. The solution pair that is closest to this pair would be the solution.
Consider b=20+400/(a-20) and b is an integer,
(a-20) has to be a factor of 400. As 16 is a factor of 400 and none of 17,18,19 is factor of 400, we can see that (a,b)=(36,45) is the pair of solution we are looking for.
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That's too hard for me :p
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a=33
b=49
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You have to include a valid method in your comment
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Yes, what is your method?
Sometimes, writing out the method will reveal an error.
I know that writing maths on a computer can be a pain - some people just do it on paper and post a photo of it - that's fine.
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