Question

1. twenty - one ounces of water evaporated from seventy - five ounces of a saline solution that had a salt concentration of 35%. find (a) the amount of salt and (b) the salt concentration in the remaining solution. round your answers to two decimal places where appropriate.

Explanation:

Step1: Calculate the amount of salt

The initial amount of the saline solution is \(75\) ounces and the salt concentration is \(35\%\).
The amount of salt \(m\) is given by the formula \(m=\text{concentration}\times\text{amount of solution}\).
So, \(m = 0.35\times75\)

$$m=26.25$$

Step2: Calculate the remaining amount of solution

The initial amount of solution is \(75\) ounces and \(21\) ounces of water evaporates.
The remaining amount of solution \(V=75 - 21=54\) ounces

Step3: Calculate the new salt concentration

The new salt concentration \(C\) is given by the formula \(C=\frac{\text{amount of salt}}{\text{remaining amount of solution}}\times100\%\)
Substitute \(m = 26.25\) and \(V = 54\) into the formula:
\(C=\frac{26.25}{54}\times 100\%\)

$$C=\frac{2625}{54}\%=\frac{875}{18}\%\approx48.61\%$$

Answer:

a. The amount of salt is \(26.25\) ounces.
b. The salt concentration in the remaining solution is approximately \(48.61\%\)