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The salt percentage of The Dead Sea has risen from 27% to 31% due to

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The salt percentage of The Dead Sea has risen from 27% to 31% due to  [#permalink]

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New post 19 Apr 2016, 13:00
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Problem:

The salt percentage of The Dead Sea has risen from 27% to 31% due to evaporation. A plan exists, where The surface of The Dead Sea would be risen by digging a canal from an ocean that has a salt percentage of 3,5%. If the volume of The Dead Sea is now V, how large quantity of The ocean's water should be led there in order for the salt percentage to be back at 27%?

Any ideas?
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Re: The salt percentage of The Dead Sea has risen from 27% to 31% due to  [#permalink]

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New post 19 Apr 2016, 22:57
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Musicat wrote:
Problem:

The salt percentage of The Dead Sea has risen from 27% to 31% due to evaporation. A plan exists, where The surface of The Dead Sea would be risen by digging a canal from an ocean that has a salt percentage of 3,5%. If the volume of The Dead Sea is now V, how large quantity of The ocean's water should be led there in order for the salt percentage to be back at 27%?

Any ideas?


Use the weighted averages concept discussed here:
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... -mixtures/

You need to mix a 3.5% solution (A1) with a 31% solution (A2) to get a 27% solution (Aavg).

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (31 - 27)/(27 - 3.5) = 4/23.5

So 4 parts of A1 should be mixed with 23.5 parts of A2.

4/23.5 = x/V

x = 40V/235 = 8V/47
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Re: The salt percentage of The Dead Sea has risen from 27% to 31% due to  [#permalink]

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New post 19 Apr 2016, 14:17
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Musicat wrote:
Problem:

The salt percentage of The Dead Sea has risen from 27% to 31% due to evaporation. A plan exists, where The surface of The Dead Sea would be risen by digging a canal from an ocean that has a salt percentage of 3,5%. If the volume of The Dead Sea is now V, how large quantity of The ocean's water should be led there in order for the salt percentage to be back at 27%?

Any ideas?

Dear Musicat,

I'm happy to respond. :-)

You may find this blog insightful:
GMAT Solution and Mixing Problems

Think about it this way.

Right now, the Dead Sea has a volume of V and a concentration of 31%, so 0.31V is pure salt and the other 0.69V is pure distilled water.

Then we add some quantity of regular ocean water, presumably from the Mediterranean Sea, so I will call this quantity M. This is the quantity for which the question asks. The regular ocean water has a concentration of 3.5%, so this means that 0.035M is pure salt and the other 0.965M is pure distilled water.

We add them, the total volume would be (V + M), and the total salt content would be (0.31V + 0.035M), and that ratio would be the concentration, which we would like to equal 27%, or 0.27.

concentration = (salt)/(total volume)

0.27 = (0.31V + 0.035M)/(V + M)

0.27V + 0.27M = 0.31V + 0.035M

0.27M - 0.035M = 0.31V - 0.27V

0.235M = 0.04V

235*M = 40*V

M = (40/235)*V = (8/47)*V

Obviously, if they add more water than that, the concentration would fall below 27%.

Does all this make sense?
Mike :-)
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Re: The salt percentage of The Dead Sea has risen from 27% to 31% due to  [#permalink]

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New post 19 Apr 2016, 19:39
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Musicat wrote:
Problem:

The salt percentage of The Dead Sea has risen from 27% to 31% due to evaporation. A plan exists, where The surface of The Dead Sea would be risen by digging a canal from an ocean that has a salt percentage of 3,5%. If the volume of The Dead Sea is now V, how large quantity of The ocean's water should be led there in order for the salt percentage to be back at 27%?

Any ideas?

By allegation you can also find as
W1/W2=(31-27)/(27-3.5)
W1/W2=4/23.5...as answer
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Re: The salt percentage of The Dead Sea has risen from 27% to 31% due to  [#permalink]

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New post 20 Apr 2016, 00:42
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w1/w2

w1 = a2-avg
w2 = avg-a1

31-27/27-3,5

This results in 4/23,5

But a decimal in the fraction is not acceptable and won't be on the gmat so you need to double it, or divide numerator and denominator by 0.5

I've taken the GMAT before and am very unhappy with myself not focusing on the weighted average concept enough, because it is not that hard and i've seen it come back 3 times on the test (which are an easy 3 points).
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Re: The salt percentage of The Dead Sea has risen from 27% to 31% due to  [#permalink]

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New post 20 Apr 2016, 11:34
Thanks to all of you, now i understand it!
Nice to see some helpful people still exist :)
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Re: The salt percentage of The Dead Sea has risen from 27% to 31% due to  [#permalink]

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Re: The salt percentage of The Dead Sea has risen from 27% to 31% due to   [#permalink] 12 Oct 2018, 15:18
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