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Snowcat [4.5K]
3 years ago
9

An urn contains 1 liter of water while a second urn nearby is empty. after 1/2 of the water in the first urn is emptied into the

second urn, 1/3 of the water in the second urn is emptied into the first urn. then, after 1/4 of the contents of the first urn is poured into the second urn, 1/5 of the contents of the second urn is poured into the first urn. at each successive pouring from alternate urns, the denominator of the fractional part poured increases by 1. how many liters of water remain in both urns after 1997th pourings
Mathematics
1 answer:
Volgvan3 years ago
3 0

We are given that there will be (1/2) a litre after the first pouring, so considering two successive pourings (n and (n+1)) with 1/2 litre in each before the nth pouring occurs:

1/2 × (1/n) = 1/(2n)

1/2 - 1/(2n) = (n-1)/2n

1/2 + 1/(2n) = (n+1)/2n

 

(n-1)/2n and (n+1)/2n in each urn after the nth pouring

 

Then now consider the (n+1)th pouring

(n+1)/2n × 1/(n+1) = 1/(2n)

(n+1)/(2n) - 1/(2n) = n/(2n) = 1/2

 

Therefore this means that after an odd number of pouring, there will be 1/2 a litre in each urn

 

Since 1997 is an odd number, then there will be 1/2 a litre of water in each urn.

 

Answer:

<span>1/2</span>

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Hi there!! Let's work!

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Prove: How many months till he has in total $300

----------------------------------------------------------------------------------------------

<h2>We need to multiply the number of months to 40 to get 300</h2>

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

<h3>So lets refer to a multiplication chart to make it easier:</h3>

||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

<h3>Here is an example of the equation we will use:</h3>

<u>400 x (months) = $300 / (or how much ever we get)</u>

```````````````````````````````````````````````````````````````````````````````````````````````````````````````````````

<h2>As you can see: </h2>

We have 2 final equations because we don't have a straight forward answer. (Refer to explanation below)

40 x 7 = 280

and

40 x 8 = 320

---------------------------------------------------------------------------------------------------------

So in problems like these we have to think like we would in real life, if you have an option you can write 7 to 8 months or you should write 8 instead of seven since they may be asking for a specific amount of months and after 8 months Gage will reach (surpass) his goal of $300 by $20.

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If you learned from my answer please rate it below from a scale of 1 to 5 using the stars to let me know how well you learned from my answer.

Make sure to also press the like button (Thanks button) if you really liked my answer / explanation

If it was incorrect or you didn't learn from it please review my answer accordingly (report if incorrect)

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I only want to spread knowledgeable and truthful information let me know if it is incorrect or not helpful so I / Brainly can take it down.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

<h3>Lastly, If your the owner of this question please mark me Brainliest if you really learned from my answer I really do appreciate it.</h3>

<h2>THANK YOU :)  </h2>

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