https://file.aiquickdraw.com/mathbot/file/1729122966862wajuvbel.jpg

The exercise is asking you to solve two parts related to ratios of paint mixtures.

### Part (a):
- You are given that for every \( \frac{1}{5} \) cup of blue paint, \( \frac{2}{5} \) cup of red paint is used, and this mixture makes 1 \( \frac{1}{5} \) gallons of purple paint.
- You are asked to determine how much red and blue paint is used.

**Step-by-step**:
1. The ratio of red to blue paint is \( \frac{2}{5} \) : \( \frac{1}{5} \), or 2:1.
2. You are making \( 1 \frac{1}{5} \) gallons of paint, which is \( \frac{6}{5} \) gallons.
3. For every 1 unit of paint mixture, 2 parts of red and 1 part of blue are used. The total number of parts in the mixture is 3 (2 parts red + 1 part blue).
4. To make \( \frac{6}{5} \) gallons of purple paint, calculate how much red and blue paint is needed by scaling the ratio to match the total gallons.

### Part (b):
- You are making a lighter purple paint by adding \( \frac{1}{10} \) cup of white paint for every \( \frac{2}{5} \) cup of red paint and \( \frac{1}{4} \) cup of blue paint.
- You are asked how much red, blue, and white paint is used to make \( \frac{3}{8} \) gallons of the lighter purple paint.

**Step-by-step**:
1. You need to maintain the given ratio of red to blue to white paint.
2. Total paint mixture consists of \( \frac{2}{5} \) cups of red paint, \( \frac{1}{4} \) cups of blue paint, and \( \frac{1}{10} \) cup of white paint.
3. Use this ratio to find out how much of each paint is required to make \( \frac{3}{8} \) gallons.

Would you like to go into more details with the calculations, or have any specific part explained?

### Related Questions:
1. What would happen if the amount of blue paint in Part (a) is doubled?
2. How do the ratios change if \( 2 \frac{1}{2} \) gallons of purple paint is needed in Part (a)?
3. What if the white paint ratio in Part (b) is increased to \( \frac{1}{5} \) per unit?
4. How do you calculate paint mixtures for different total volumes of paint?
5. How can you simplify the ratio calculations for larger volumes?

### Tip:
Always remember to convert mixed numbers into improper fractions before scaling ratios!

You mix 2/5 cup of red paint for every 1/5 cup of blue paint to make 1 1/5 gallons of purple paint. a. How much red paint and blue paint do you use? b. You decide that you want to make a lighter purple paint. You make the new mixture by adding 1/10 cup of white paint for every 2/5 cup of red paint and 1/4 cup of blue paint. How much red paint, blue paint, and white paint do you use to make 3/8 gallon of lighter purple paint?

This problem involves solving paint mixture ratios to determine the quantities of red, blue, and white paint needed to create 1 1/5 gallons of purple paint and 3/8 gallon of lighter purple paint. Learn how to apply ratios, proportions, and fraction concepts in this detailed solution 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