A lab technician has a 40% alcohol solution and a 60% alcohol solution. He needs to make 1000 grams of a solutionthat is 48%
alcohol.
5. How much of the 40% alcohol solution should he use?
A. 300 grams
B. 400 grams
C. 500 grams
D. 600 grams
E. 700 grams

This problem can be solved using the concept of a weighted average or mixture problem. Let's define the variables first:

- Let \( x \) be the amount (in grams) of the 40% alcohol solution.
- Since the technician needs to make a total of 1000 grams of solution, the amount of the 60% alcohol solution will be \( 1000 - x \).

The next step is to set up an equation based on the amount of alcohol in the mixture.

1. The amount of alcohol in the 40% solution is \( 0.40x \).
2. The amount of alcohol in the 60% solution is \( 0.60(1000 - x) \).
3. The total amount of alcohol in the final solution should be 48% of 1000 grams, which is \( 0.48 \times 1000 = 480 \) grams.

Now, we can set up the equation:

\[
0.40x + 0.60(1000 - x) = 480
\]

Simplify and solve for \( x \):

\[
0.40x + 600 - 0.60x = 480
\]

Combine like terms:

\[
-0.20x + 600 = 480
\]

Subtract 600 from both sides:

\[
-0.20x = -120
\]

Now, divide by \(-0.20\):

\[
x = \frac{-120}{-0.20} = 600
\]

Thus, the technician should use **600 grams** of the 40% alcohol solution.

The correct answer is:

**D. 600 grams**

Would you like more details or have any questions?

### Related Questions:
1. How much of the 60% alcohol solution should the technician use?
2. What if the desired concentration was 50% alcohol? How would the solution change?
3. How would the solution change if only 500 grams of final solution were needed?
4. What is the general formula for solving mixture problems like this one?
5. How can you check if the solution is correct?

### Tip:
Always double-check your units when working with mixture problems to ensure consistency throughout the calculations.

A lab technician has a 40% alcohol solution and a 60% alcohol solution. He needs to make 1000 grams of a solution that is 48% alcohol. How much of the 40% alcohol solution should he use?

Learn how to solve a common mixture problem involving a 40% and a 60% alcohol solution. The problem involves algebraic methods, including setting up and solving a mixture equation to find the correct amounts needed for a final 48% alcohol solution. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation