https://file.aiquickdraw.com/mathbot/file/1727970738914lybzr0fy.jpg

Let's go through the math problems from the image.

### 1. Chocolate Milk Proportional Relationship
The table shows how Han mixes chocolate syrup and milk to make different-sized batches of chocolate milk. 

We are given:
- 2 cups of milk require 3 tablespoons of syrup.
- The table extends this ratio to larger or smaller quantities.

#### a. **Proportional Relationship**
The table shows a proportional relationship between **cups of milk** and **tablespoons of chocolate syrup**.

Answer: \( 3 \) and \( 2 \)

#### b. **Scale Factor**
To find the scale factor between 2 cups of milk and 8 cups of milk, we can see that 8 is 4 times larger than 2.

Answer: \( 4 \)

#### c. **Constant of Proportionality**
The constant of proportionality is the ratio of tablespoons of syrup to cups of milk. From the given dataLet's go through the math problems from the image.

### 1. Chocolate Milk Proportional Relationship
The table shows how Han mixes chocolate syrup and milk to make different-sized batches of chocolate milk. 

We are given:
- 2 cups of milk require 3 tablespoons of syrup.
- The table extends this ratio to larger or smaller quantities.

#### a. **Proportional Relationship**
The table shows a proportional relationship between **cups of milk** and **tablespoons of chocolate syrup**.

Answer: \( 3 \) and \( 2 \)

#### b. **Scale Factor**
To find the scale factor between 2 cups of milk and 8 cups of milk, we can see that 8 is 4 times larger than 2.

Answer: \( 4 \)

#### c. **Constant of Proportionality**
The constant of proportionality is the ratio of tablespoons of syrup to cups of milk. From the given 
\[
\frac{3 \text{ tablespoons}}{2 \text{ cups}} = \frac{3}{2}
\]

Answer: \( \frac{3}{2} \)

#### d. **Units for Constant of Proportionality**
The constant of proportionality \( \frac{3}{2} \) describes the ratio of **tablespoons of syrup per cup of milk**.

Answer: \( \text{tablespoons per cup of milk} \)

### 2. Paint Mixing Proportional Relationship
Here, we are looking at the proportional relationship between red paint and white paint.

#### a. **Cups of Red Paint for 1 Cup of White Paint**
According to the table, for 7 cups of white paint, we need 3 cups of red paint. To find how much red paint is needed for 1 cup of white paint, we set up a proportion:
\[
\frac{7}{3} = \frac{1}{x}
\]
Solving for \( x \), we get:
\[
x = \frac{3}{7}
\]
So, for 1 cup of white paint, you would need \( \frac{3}{7} \) cups of red paint.

Answer: \( \frac{3}{7} \) cups of red paint

#### b. **Constant of Proportionality**
The constant of proportionality is the ratio of red paint to white paint, which from the table is:
\[
\frac{3}{7}
\]

Answer: \( \frac{3}{7} \)

---

Do you want further details on any specific part or have questions?

Here are 5 relative questions to expand on this:

1. How do you calculate the constant of proportionality in general?
2. What does the constant of proportionality tell us about a relationship?
3. If you double the amount of milk, how many tablespoons of syrup would be needed?
4. How could you apply proportions to solve real-world mixing problems like paint or food recipes?
5. Why is the relationship between milk and syrup described as proportional?

**Tip:** When working with proportions, always keep track of the units to avoid confusion, especially when scaling up or down!

When Han makes chocolate milk, he mixes 2 cups of milk with 3 tablespoons of chocolate syrup. The table shows how to make different batch sizes, and questions about proportional relationships, scale factor, constant of proportionality, and units are asked. The second problem involves mixing paint in a proportional relationship between red and white paint.

Explore how to solve proportional relationship problems, including calculating the constant of proportionality and scale factor. This example features chocolate milk mixing and paint mixing ratios, demonstrating practical applications of proportions. Suitable for middle school students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation