Salt water problem

gavroche

New member
Joined
Jan 12, 2015
Messages
6
A 18 gallon salt water solution contains 15% pure salt. How much water should be added to produce the solution to 12% salt?

This is what I tried:

18 * 0.85 = 15.3, the amount of water in the solution, so:

15.3 / 18 = 85 / 100 -> The amount of water in the solution equals 85% (100-15 pure salt)


x / 18 = 88 / 100 (88% is the amount of water required to have 12% salt in the water. 100 - 12 = 88)

x = 15.84, so the amount of water needed to be added is 0.54

However, that is not the correct answer, the correct answer is 4.5

FORGOT TO MENTION: The water is measured in gallons, if it helps anyone.
 
A 18 gallon salt water solution contains 15% pure salt. How much water should be added to produce the solution to 12% salt?

This is what I tried:

18 * 0.85 = 15.3, the amount of water in the solution, so:

15.3 / 18 = 85 / 100 -> The amount of water in the solution equals 85% (100-15 pure salt)


x / 18 = 88 / 100 (88% is the amount of water required to have 12% salt in the water. 100 - 12 = 88)

x = 15.84, so the amount of water needed to be added is 0.54

However, that is not the correct answer, the correct answer is 4.5

FORGOT TO MENTION: The water is measured in gallons, if it helps anyone.
You have two containers (one with 18 gallons with 15% salt and a second one with x gallons and 0% salt solution.) You mix the two containers and end up with (18+x) gallons with 12% solution. Can you finish from here?
 
Nothing I try works... I guess I am now stuck at the point where:

18 + x is the new total solution, and y would be the salt in that so:

y / (18 + x) = 12 / 100

but nothing...
 
A 18 gallon salt water solution contains 15% pure salt. How much water should be added to produce the solution to 12% salt?

This is what I tried:

18 * 0.85 = 15.3, the amount of water in the solution, so:

15.3 / 18 = 85 / 100 -> The amount of water in the solution equals 85% (100-15 pure salt)


x / 18 = 88 / 100 (88% is the amount of water required to have 12% salt in the water. 100 - 12 = 88)

x = 15.84, so the amount of water needed to be added is 0.54

However, that is not the correct answer, the correct answer is 4.5

FORGOT TO MENTION: The water is measured in gallons, if it helps anyone.

Total salt in first solution = 18*0.15*k (k is the conversion factor for gallons to lbs etc.)

Total salt in final solution = (18+x)*0.12*k

Since amount of salt remains the same:

18*0.15*k = (18+x)*0.12*k

0.12 * x = 0.03 * 18 → x = ???
 
Nothing I try works... I guess I am now stuck at the point where:

18 + x is the new total solution, and y would be the salt in that so:

y / (18 + x) = 12 / 100

but nothing...
The amount of pure salt in the two containers must equal the amount of salt in the mixture of these two container.

If you mix two containers and one container has 3 gallons of liquid and the other container has 5 gallons of liquid then the mixture has 3+5 gallons or 8 gallons

So if you mix two containers and one container has 18 gallons of liquid and the other container has x gallons of liquid then the mixture has (18+x) gallons of liquid.

The 1st container has 18(15%)=2.7 gallons of pure salt.
The 2nd container (which is all water, so 0% of salt) has x(0%)=0 gallons of salt.
So combined we have 2.7 gallons of pure salt.

Now onto the mixture. We have (18+x)(12%)= 2.16 + .12x

Just equate the two: 2.7 = 2.16 + .12x. Multiply by 100 to get rid of decimals (if you like). Then have 270= 216 + 12x.....x=4.5
 
Top