Solve without a calculator – 1

Algebra Level 2

Convert 55 miles into kilometers and round to the nearest whole kilometer.


The answer is 89.

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2 solutions

55 × 1.609 55\times 1.609 nearly equals ( 100 2 + 10 2 ) × 1.61 = ( 161 + 16.1 ) 2 = 88.55 (\dfrac {100}{2}+ \dfrac {10}{2})\times 1.61 = \dfrac {(161 + 16.1 )}{2} = 88.55

A N S W E R : [ 88.55 ] = 89 ANSWER:[88.55] = \boxed {89}

That's a very clever solution! Didn't think of it

Henry U - 2 years, 6 months ago

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That's how I calculate on usual basis.If anyone doesnt know much about Fibonacci and Lucas numbers,they can use this. Cool, right?!

A Former Brilliant Member - 2 years, 6 months ago

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Indeed, especially that you only had to multiply by 10 and divide by 2 which is really simple.

Henry U - 2 years, 6 months ago

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@Henry U That's the trick!! LIFE IS SIMPLE AND FUN!!. Hence, proved!

A Former Brilliant Member - 2 years, 6 months ago
Henry U
Nov 14, 2018

One mile corresponds to 1.609344 1.609344 kilometers, which is close to the golden ratio ϕ 1.618 \phi \approx 1.618 . ϕ \phi also happens to be the ratio between consecutive Fibonacci numbers and fortunately, 55 55 is a Fibonacci number. To convert into kilometers, just take the next Fibonacci number which is 89 89 .

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