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# Algebra

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I have two one-quart jars; the first is filled with water, and the second is empty. I pour half of the water in the first jar into the second, then a third of the water in the second jar into the first, then a fourth of the water in the first jar into the second, then a fifth of the water in the second jar into the first, and so on. How much water in quarts is in the first jar after the 10th pour? Express your answer as a common fraction.

Thanks

Aug 31, 2020

#1
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OK Kiddo! This is the best I came up with. Maybe others will try it:

1 - 1/2 =1/2+(1/3*1/2)=2/3 - (1/4*2/3)=1/2+(1/5*1/2)=3/5 - (1/6*3/5) =1/2+(1/7*1/2)=4/7 - (1/8*4/7)=1/2+(1/9*1/2) =5/9 - (1/0*5/9) =1/2 - This is what is left in the first jar after 10 pourings!!

Aug 31, 2020
#2
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(?????)

"OK Kiddo"??? who are you to say that?

Plus, 1/2 is definitely not correct - just use logic; the first jar has 1/2 quart in it after pouring 1/2 into the second jar, then the second jar gives 1/3 * 1/2 = 1/6 back, then it keeps going back and forth so it would never be EXACTLY 1/2, even if it might come close.

plus, 1/0 is undefined, and in your sol you multiply it by 5/9 and subtract that from 5/9 to get... 1/2 !!! Welp i guess I learned something new today!

Guest Sep 6, 2020