A solution contains 6% salt. How much water should be added to 30 ounces of this solution to make a 1.8% solution ?

Question

I need help solving this word problem 

Answer 1

concentration = (amt of salt) / (amt of solution).

We start with 30 oz. of solution, which is 6% salt.  We have to treat percentages as decimals to answer the problem.  The amount of salt is then 6% of 30 ounces, or (.06)(30) = 1.8.

 

In pure water, there is no salt.  Let x be the amount of pure water added to the solution.

 

We now have (amount of solute)/(amount of solution)

=1.8/(30 + x)

 

But this must be a 1.8% solution; in other words, (amount of solute)/(amount of solution) = .018

 

From these facts we can make an equation:

 

1.8/(30 + x) = .018

 

To clear the fraction, multiply both sides by (30 + x):

1.8 = .018(30 + x).  Distribute the .018 on the right-hand side:

1.8 = .54 + .018x.  Subtract .54 from both sides:

1.26 = .018x.  Divide both sides by .018:

70 = x

 

You must add 70 oz of pure water to end up with a 1.8% solution.

 

1800(30 + x) = 18

Now, divide both sides by 18:

1000(30 + x) = 1.  Distribute:

30,000 + 1000x = 1