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

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.

1/2

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt