Intriguing fraction
Work out x
How did you do it?
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Simple to simplify?
This is a lovely question that I was emailed by brilliant.org If you haven't seen that site then do go there. I suggest signing up for the free access and having fun exploring some of their frankly brilliant problems. This one involves some nice techniques and will allow you to delve into different A-level maths ideas.
a=4, b=6, c=7
ReplyDeleteI found the factors of 84 to be 2×2×3×7 and then played around and found that 1/2 + 1/2×6 + 1/2×6×7 is equal to 50/84. I wanted the denominator to be 2×84 so that the fraction could equal 25/84. So I multiplied 1/2 + 1/2×6 + 1/2×6×7 by 1/2 to find that 1/4 + 1/24 + 1/168 works. Therefore a=4, ab=24, abc=168 following that the triplet is (4,6,7) and a+b+c is 17. Is there another way to do it?
The factors idea is a good one. Well spotted with 50/84. I used a different method and got the same answer as you. (And then used another method too!).
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