https://file.aiquickdraw.com/mathbot/file/1726279238109ih5u3tg3.jpg

This is a mixture problem where we need to calculate how many gallons of pure water and how many gallons of the premium antifreeze solution are required.

Let's define:
- \( x \) as the number of gallons of the premium antifreeze solution (which is 80% antifreeze).
- \( y \) as the number of gallons of water (which is 0% antifreeze).

The total mixture will be 160 gallons and it needs to contain 70% antifreeze. The premium antifreeze solution contains 80% antifreeze, and pure water contains 0% antifreeze.

We can set up the following two equations based on this information:

1. **Total gallons equation** (for the entire mixture):
   \[
   x + y = 160
   \]
2. **Antifreeze concentration equation** (for the amount of pure antifreeze in the final mixture):
   \[
   0.80x + 0.00y = 0.70 \times 160
   \]

Now, I will solve these equations.The chemical company needs to mix **140 gallons of the premium antifreeze solution** with **20 gallons of water** to obtain 160 gallons of a mixture that contains 70% pure antifreeze.

Would you like more details or have any further questions?

Here are 5 related questions:
1. What if the company wants a 50% antifreeze solution instead of 70%?
2. How would the mixture change if the premium antifreeze solution were only 60% pure?
3. What if the final desired mixture was 200 gallons instead of 160 gallons?
4. How would the calculations change if the water was not pure, but contained some antifreeze?
5. How can this problem be modeled graphically?

**Tip:** Mixture problems often involve setting up equations based on total volume and concentration percentages. Solving these equations simultaneously will give you the required quantities.

A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 80% pure antifreeze. The company wants to obtain 160 gallons of a mixture that contains 70% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be mixed?

Learn how to solve a mixture problem where a chemical company mixes water and 80% premium antifreeze solution to obtain 160 gallons of a 70% pure antifreeze mixture. This example demonstrates the use of algebra and systems of equations, ideal for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation