How much water must be evaporated from 36 ounces of an 8 % salt solution to make a 9 % salt​ solution?

To solve the problem, we'll use the concept of concentration by mass. Here's the step-by-step process:

### Step 1: Calculate the initial amount of salt in the solution.
The initial solution is 36 ounces with 8% salt. The amount of salt in the solution is:

\[
\text{Amount of salt} = 36 \text{ ounces} \times \frac{8}{100} = 2.88 \text{ ounces of salt}
\]

### Step 2: Set up the equation for the final solution.
Let \( x \) be the amount of water that needs to be evaporated.

After evaporating \( x \) ounces of water, the new volume of the solution is \( 36 - x \) ounces. The amount of salt remains the same, but now it is dissolved in a smaller amount of water, increasing the concentration.

We want the final concentration to be 9%, so:

\[
\frac{2.88 \text{ ounces of salt}}{36 - x \text{ ounces of solution}} = \frac{9}{100}
\]

### Step 3: Solve for \( x \).
To solve for \( x \), multiply both sides by \( 36 - x \):

\[
2.88 = 0.09 \times (36 - x)
\]

Distribute the 0.09:

\[
2.88 = 3.24 - 0.09x
\]

Isolate \( x \) by subtracting 3.24 from both sides:

\[
2.88 - 3.24 = -0.09x
\]

\[
-0.36 = -0.09x
\]

Divide by -0.09:

\[
x = \frac{-0.36}{-0.09} = 4 \text{ ounces}
\]

### Conclusion
You need to evaporate **4 ounces** of water from the solution to increase the concentration to 9%.

Would you like more details or have any questions?

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Here are 5 related questions for further practice:
1. How much water should be added to a 10% salt solution to dilute it to 5%?
2. If 5 ounces of water is evaporated from a 50-ounce 7% salt solution, what will be the new concentration?
3. How much salt is in a 15% solution if you have 40 ounces of it?
4. If a solution has 3 ounces of salt and 17 ounces of water, what is the concentration?
5. How would the concentration change if instead of evaporating water, 10 ounces of water were added to the original solution?

**Tip:** When working with concentration problems, keep in mind that the amount of solute (in this case, salt) stays constant unless more solute is added or removed.

Learn how to adjust the concentration of a salt solution by evaporating water. Solve the problem step-by-step to find out how much water must be evaporated from a 36-ounce, 8% salt solution to achieve a 9% concentration. Suitable for high school level students studying concentration by mass and percentage calculations.

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