Question

Please help!

Use the four-step procedure to solve the following problem.

How much water must be added to a gallon of 10% saline solution to create a 2% solution?

1. There is 1 gallon of
% solution.
2. There is
% saline in water.
3. The equation is
.
4. The answer is
gallons.

Answer 1

step 1: there is 1 gallon of __% solution

this is already given in the problem (the saline is 10%)

step 2: there is __% saline in water

for simplicity's sake, let's assume this is pure water, and thus 0% saline

step 3: now, this is the complicated part. we want a solution that is 2% saline, or in other words:

(total amount of salt/total amount of solution) = 2%, or 0.02

let's let x = the amount of water that we will add to the solution

we already have 1 gallon of 10% solution, which is 10% * 1 = 0.1 gallon of salt

when we add water, we're not adding any new salt, but we will add to the total amount of solution.

currently, with 1 gallon of 10% saline, we have 1 gallon of solution and we will add x onto it.

therefore, the denominator is x + 1

making our equation 0.02 = 0.1/(x+1)

(I know this is a lot, so please let me know if anything was unclear)

step 4: solve the equation from step 3