SOLUTION: Cucumbers are on sale, so you buy 29 pounds of them at the local market for your restaurant. Each cucumber is actually 99% water. A few days later, the cucumbers have dried out to

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Question 1120477: Cucumbers are on sale, so you buy 29 pounds of them at the local market for your restaurant. Each cucumber is actually 99% water. A few days later, the cucumbers have dried out to the point that each is now 91% water. How much do all your cucumbers weigh at this time?
Found 5 solutions by Boreal, rothauserc, ikleyn, greenestamps, Shin123:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
29/0.99=x/0.91
cross multiply
26.66 pounds
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
29 * 0.99 = 28.71 lbs
:
therefore 28.71 lbs of the cucumbers is water
:
0.99/28.71 = 0.91/x
:
x = (0.91 * 28.71)/0.99 = 26.39
:
29 - 28.71 = 0.29 lbs does not change
:
new weight of cucumbers is 26.39 + 0.29 = 26.68 lbs
:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

The solutions to this problem given by the two respectful tutors @Boreal and @rothauserc are irreparably and fatally wrong.

They would be correct, had the dry component of the cucumbers went out with the water at the drying process.

But it is not so: the dry component remains in the place.

Below find the correct solution. 

    29 pounds of cucumbers contained initially/originally  0.99*29 = 28.71 pounds of water and 29 - 28.71 = 0.29 of a pound of the dry substance.


    Let w be the amount of the water in cucumbers when their water content is 91%.


    It means that the ratio of the water content "w" to the total amount of (0.29+w) pounds is 0.91:


         = 0.91,   or

        w = 0.91*(0.29 + w),

        w - 0.91*w = 0.91*0.29,

        w*0.09 = 0.91*0.29  ====>  w =  = 2.93 pounds.


    Hence, after drying your cucumbers weight  0.29 + 2.93 = 3.22 pounds.


    Answer.  After drying your cucumbers weight  3.22 pounds.

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Absolutely unexpected result ?   -   Yes,  I totally agree.

Let's check the final water content.   It is   2.93/3.22 = 0.91.       ! Correct !


It is a classic entertainment problem, which leads to very unexpected answer.

Specially for such problems,  I developed the lesson
    - Problems on percentage that lead to unexpected results
in this site,  where similar problems were solved and explained in all details.

===================

I am glad to use this opportunity to teach you on how to solve such problems correctly.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Yes, this problem has an answer that seems unreasonable.... But tutor @ikleyn's answer is right.

Here is another way to find that answer.

(1) Initially, the cucumbers are 99% water, so the "meat" of the cucumber is only 1%.
(2) So in 29 pounds of cucumbers, the meat is only 0.29 pounds.
(3) When the cucumbers have dried out, they are now 91% water, which means they are now 9% meat.
(4) The same original 0.29 pounds of meat is now 9% of the total weight:



The new total weight, to 2 decimal places, is 3.22 pounds.
Answer by Shin123(626)   (Show Source): You can put this solution on YOUR website!
After the water has dried out, the 29*0.01=0.29 pounds are still dry.0.29 pounds are 9% now. If 0.29 is 9%, then 0.29/9 is 1% and 29/9 is 100%. The cucumbers now weigh 3.22222... pounds, or 3.22 pounds rounded.
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