SOLUTION: With each stroke, a pump removes {{{1/6}}} of the air in a container. After 6 strokes, what is the fraction of the original amount of air in the container that is left?

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Question 1204285: With each stroke, a pump removes of the air in a container. After 6 strokes, what is the fraction of the original amount of air in the container that is left?
Found 3 solutions by ikleyn, MathLover1, math_tutor2020:
Answer by ikleyn(52852)   (Show Source): You can put this solution on YOUR website!
.

After 1st stroke, 5/6   of the initial air mass remains;

After 2nd stroke,  of the initial air mass remains;

After 3rd stroke,  of the initial air mass remains;

After 4th stroke,  of the initial air mass remains;

After 5th stroke,  of the initial air mass remains;

After 6th stroke,  of the initial air mass remains, or  0.3349  of the initial air mass remains  (rounded).    ANSWER

Solved.


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https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.75801.html

at this forum.


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Regarding the post by @MathLover1, I recall this medical proverb:

            a drop of nicotine kills a horse.


Likewise, @MatnLover1's answer may kill a reader.
He will die if not from horror to have such a  " tutor ",  then from laughter.


            So,  for safety of your mind,  you better ignore her post.




Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

the amount of full container:
stroke, a pump removes of the air in a container

strokes


=> container is practically empty
so, the original amount of air in the container that is left is



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: 15625/46656
Which is the same as writing

How to get that answer:
With one stroke, 1/6 of the air is removed, so 5/6 of the air remains.
Do this 6 times to get (5/6)^6 = (5^6)/(6^6) = 15625/46656

When converting to decimal form,
15625/46656 = 0.3349 = 33.49% approximately
Roughly 33.49% of the original air remains inside the container.

Personally I think a percentage is the best way to represent the final answer, but you should stick to the fraction form since that's what the instructions state.

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