Question 1161827: In a tropical fish store, one tank contains 65 kilograms of seawater with 7% salt.
a. How much pure water must be added to have 5% salt?
b. How much water must be evaporated to contain 9% salt?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you start with 65 kilograms of seawater that is 7% salt.
that means that 7% of the seawater is salt and 93% of the seawater is pure water.
that means you have 4.55 kilograms of salt and 60.45 kilograms of pure water.
if you want to get 5% seawater, you have to add pure water.
if you want to get 9% seawater, you have to add salt.
we'll use the variable called x to determine the amount of pure water to add to get 5% seawater and then we'll use the variable called x to determine the amount of salt to add to get 9% seawater.
if you want 5% seawater, than you have to have 95% pure water.
your first equation is therefore:
.95 * (65 + x) = 60.45 + x
solve this equation and you will get x = 26 kilograms.
60.45 + 26 = 86.45 kilograms of pure water.
add 4.55 kilograms of salt (you didn't add any more salt to the mixture, only pure water) to get 91 kilograms of seawater.
86.45 / 91 = .95 = 95% pure water.
that means 5% salt which is what you want.
if you want 9% salt, then your second equation becomes:
.09 * (65 + x) = 4.55 + x
solve this equation and you will get x = 1.428571429 kilograms.
4.55 + x = 5.978571q429 kilograms of salt.
add 60.45 kilograms of water (you didn't add any pure water to the mixture, only salt) to get 65.97857143 kilograms of seawater.
4.978571429 / 65.97857143 = .09 = 9% salt.
your solutions are therefore.
add 26 kilograms of pure water to 65 kilograms of seawater that is 7% salt to get 91 kilograms of seawater that is 5% salt.
add 1.428571429 kilograms of salt to 65 kilograms of seawater that is 7% salt to get 65.97857143 kilograms of seawater that is 9% salt.
HOWEVER, .....
you were not asked to add salt to get seawater that is 9% salt.
you were asked to evaporate pure water to get seawater that is 9% salt.
that's a different equation.
that equation is:
60.45 - x = .91 * (65 - x)
you are evaporating x kilograms of pure water from a mixture that is 93% pure water to get a mixture that is 91% pure water, making it 9% salt.
solve this equation and you will get x = 14.4444444.....
60.45 - x = 46.0055555... kilograms of pure water that has not been evaporated and is therefore left in the mixture.
65 - x = 50.555555..... kilograms of seawater that is left after the pure water has been evaporated.
46 .0055555..... / 50.55555.... = .91 = 91% pure water.
that makes the mixture 9% salt.
so your solutions become:
add 26 kilograms of pure water to 65 kilograms of seawater that is 7% salt to get 91 kilograms of seawater that is 5% salt.
evaporate 14.44444.... kilograms of pure water from seawater that is 7% salt to get 50.55555..... kilograms of seawater that is 9% salt.
in both cases, the amount of salt was not changed. the only changes was in the amount of pure water in the mixture.
Answer by ikleyn(52787)  (Show Source):
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