https://file.aiquickdraw.com/mathbot/file/1725947831895mm3618rs.jpg

The problem written on the board states:

"Rachel mixes 5 gallons of a 20% antifreeze solution with 10 gallons of a 50% antifreeze solution with a different antifreeze concentration.
- (a) Will the new solution have a concentration that is closer to 20% or 50%?
- (b) Calculate the concentration of the new antifreeze solution."

### Let's solve the problem:

1. **Total antifreeze content in the mixture:**
   - **From the 20% solution**: \( 5 \text{ gallons} \times 20\% = 5 \times 0.2 = 1 \text{ gallon of antifreeze} \)
   - **From the 50% solution**: \( 10 \text{ gallons} \times 50\% = 10 \times 0.5 = 5 \text{ gallons of antifreeze} \)

2. **Total volume of the solution:**
   - Total volume = \( 5 \text{ gallons} + 10 \text{ gallons} = 15 \text{ gallons} \)

3. **Total antifreeze content in the new solution:**
   - Total antifreeze = \( 1 \text{ gallon} + 5 \text{ gallons} = 6 \text{ gallons of antifreeze} \)

4. **Concentration of the new solution:**
   - Concentration \( = \frac{\text{total antifreeze}}{\text{total volume}} = \frac{6 \text{ gallons}}{15 \text{ gallons}} = 0.4 \text{ or } 40\% \)

### Answers:
- (a) The concentration of the new solution is **closer to 50%** (because the result is 40%).
- (b) The concentration of the new solution is **40%**.

Would you like further details or have any other questions?

Here are 5 related questions to expand your understanding:
1. How would the concentration change if Rachel used 5 gallons of the 50% solution instead of 10 gallons?
2. What happens if the volumes of both solutions are equal (e.g., 5 gallons of each)?
3. How would the final concentration be affected if one of the solutions had a 100% concentration of antifreeze?
4. How would the concentration be calculated if the antifreeze was mixed with water instead of another antifreeze solution?
5. What is the effect of adding a 0% concentration solution (pure water) on the final concentration?

**Tip**: When solving mixture problems, always compute the total amount of the substance (like antifreeze) in the mixture first, and then divide by the total volume to get the concentration.

Rachel mixes 5 gallons of a 20% antifreeze solution with 10 gallons of a 50% antifreeze solution. (a) Will the new solution have a concentration that is closer to 20% or 50%? (b) Calculate the concentration of the new antifreeze solution.

Explore how to calculate the concentration of a mixture of antifreeze solutions, combining 5 gallons of 20% solution and 10 gallons of 50% solution. Learn how to determine whether the new concentration is closer to 20% or 50%.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation