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Let's go through each of the problems step by step to provide solutions.

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### Problem 1:
The table shows a proportional relationship between the number of cups of water (x) and pancake mix (y).

| Cups of Water (x) | Cups of Pancake Mix (y) |
|------------------|-------------------------|
| 1                | 2                       |
| 3                | 6                       |
| 6                | 12                      |

- **a)** Enter the number of cups of pancake mix used for 1 cup of pancake mix.  
  From the table, for every 1 cup of water, there are **2 cups of pancake mix**.

- **b)** Enter the constant of proportionality that relates the quantities \( x \) and \( y \).  
  The constant of proportionality (k) is the ratio \( \frac{y}{x} \). From the table,  
  \( k = \frac{2}{1} = 2 \).

- **c)** Enter an equation that relates the quantities.  
  Since \( y = kx \), the equation is \( y = 2x \).

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### Problem 2:
The table shows a proportional relationship between the number of cups of chocolate powder (x) and milk (y).

| Cups of Chocolate Powder (x) | Cups of Milk (y) |
|------------------------------|------------------|
| 4                            | 5                |
| 12                           | 15               |
| 15                           | 20               |

- **a)** Enter the number of cups of chocolate powder used for 1 cup of milk.  
  To find this, we need to use the ratio from the table. From row 1:  
  \( \frac{4}{5} \), so **0.8 cups of chocolate powder** is used for 1 cup of milk.

- **b)** Enter the constant of proportionality that relates the quantities \( x \) and \( y \).  
  Using the ratio \( k = \frac{y}{x} = \frac{5}{4} = 1.25 \), the constant of proportionality is **1.25**.

- **c)** Enter an equation that relates the quantities.  
  The equation is \( y = 1.25x \).

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### Problem 3:
The table shows a proportional relationship between the number of cups of peach juice (x) and lemonade (y).

| Cups of Peach Juice (x) | Cups of Lemonade (y) |
|-------------------------|----------------------|
| 4                       | 6                    |
| 12                      | 18                   |
| 20                      | 30                   |

- **a)** Enter the number of cups of peach juice used for 1 cup of lemonade.  
  Using the ratio from the first row: \( \frac{4}{6} = 0.67 \). So, **0.67 cups of peach juice** are used for 1 cup of lemonade.

- **b)** Enter the constant

The table shows proportional relationships between different quantities, asking for the constant of proportionality, the equation relating the quantities, and specific values for given amounts.

Learn how to find the constant of proportionality and write equations for proportional relationships. These problems involve proportional tables of various quantities like water, pancake mix, chocolate powder, and more. Suitable for students in Grades 6-8.

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