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 ProblemsThink 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)*VObviously, if they add more water than that, the concentration would fall below 27%.
Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)