2 gal.of an acid solution was mixed with 4 gal of a 85% acid solution to make a 60% acid solution.Find the present concentration of the first solution 

Let the concentration of the first acid solution be \( x \% \). The total amount of acid in the mixture can be expressed as:

- Acid from the first solution: \( 2 \times \frac{x}{100} \) gallons
- Acid from the second solution (85% acid): \( 4 \times \frac{85}{100} = 3.4 \) gallons

The total volume of the mixture is \( 2 + 4 = 6 \) gallons, and the final concentration is 60%, meaning that the total acid content in the mixture is:

\[
6 \times \frac{60}{100} = 3.6 \text{ gallons of acid.}
\]

Now, we can set up the equation for the total amount of acid:

\[
2 \times \frac{x}{100} + 3.4 = 3.6
\]

Solve for \( x \):

\[
2 \times \frac{x}{100} = 3.6 - 3.4
\]
\[
2 \times \frac{x}{100} = 0.2
\]
\[
\frac{x}{100} = \frac{0.2}{2}
\]
\[
\frac{x}{100} = 0.1
\]
\[
x = 10
\]

Thus, the concentration of the first solution is \( 10\% \).

Would you like further details or have any questions?

Here are five related questions:
1. How do we calculate the concentration of a solution given the amount of solute and solvent?
2. What is the general formula for mixing solutions of different concentrations?
3. How would the solution change if the volume of the first solution were different?
4. How can we derive the concentration for more than two solutions?
5. What happens to the final concentration if a diluting substance is added?

**Tip**: When mixing solutions, always ensure that the units for volume and concentration are consistent throughout the calculations.

2 gal. of an acid solution was mixed with 4 gal of an 85% acid solution to make a 60% acid solution. Find the present concentration of the first solution.

Learn how to solve a mixture problem where 2 gallons of an unknown acid concentration are mixed with 4 gallons of an 85% acid solution to form a 60% acid solution. This step-by-step solution explains how to calculate the concentration of the first solution using algebra and percentage calculations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation