Matching worksheet for identifying proportional relationships in real-world scenarios.

Problem Description:

The task is to match the given data tables to their corresponding constants of proportionality. The problem involves identifying whether the quantities in each table are proportional and, if so, determining the constant of proportionality.

Given Data Tables:

1. Jean eats bananas over time:
- Minutes: 5, 10, 15, 20, 25
- Number of Bananas: 7, 14, 21, 28, 35

2. Norman made cakes and used cream:
- Number of Cakes: 3, 6, 9, 12, 15
- Cream (grams): 6, 12, 18, 24, 30

3. Donald played card games over time:
- Number of Games Played: 4, 8, 12, 16, 20
- Minutes: 10, 20, 30, 40, 50

Solution Approach:

To determine if the quantities in each table are proportional, we need to check if the ratio between the two quantities remains constant for all pairs of values. If the ratio is constant, the quantities are proportional, and the constant of proportionality is that ratio.

#### Step 1: Analyze Table 1 (Jean eats bananas over time)
- Minutes: 5, 10, 15, 20, 25
- Number of Bananas: 7, 14, 21, 28, 35

Calculate the ratio of "Number of Bananas" to "Minutes":
\[
\text{Ratio} = \frac{\text{Number of Bananas}}{\text{Minutes}}
\]
- For the first pair: \( \frac{7}{5} = 1.4 \)
- For the second pair: \( \frac{14}{10} = 1.4 \)
- For the third pair: \( \frac{21}{15} = 1.4 \)
- For the fourth pair: \( \frac{28}{20} = 1.4 \)
- For the fifth pair: \( \frac{35}{25} = 1.4 \)

Since the ratio is constant (1.4), the quantities are proportional, and the constant of proportionality is 1.4.

#### Step 2: Analyze Table 2 (Norman made cakes and used cream)
- Number of Cakes: 3, 6, 9, 12, 15
- Cream (grams): 6, 12, 18, 24, 30

Calculate the ratio of "Cream (grams)" to "Number of Cakes":
\[
\text{Ratio} = \frac{\text{Cream (grams)}}{\text{Number of Cakes}}
\]
- For the first pair: \( \frac{6}{3} = 2 \)
- For the second pair: \( \frac{12}{6} = 2 \)
- For the third pair: \( \frac{18}{9} = 2 \)
- For the fourth pair: \( \frac{24}{12} = 2 \)
- For the fifth pair: \( \frac{30}{15} = 2 \)

Since the ratio is constant (2), the quantities are proportional, and the constant of proportionality is 2.

#### Step 3: Analyze Table 3 (Donald played card games over time)
- Number of Games Played: 4, 8, 12, 16, 20
- Minutes: 10, 20, 30, 40, 50

Calculate the ratio of "Minutes" to "Number of Games Played":
\[
\text{Ratio} = \frac{\text{Minutes}}{\text{Number of Games Played}}
\]
- For the first pair: \( \frac{10}{4} = 2.5 \)
- For the second pair: \( \frac{20}{8} = 2.5 \)
- For the third pair: \( \frac{30}{12} = 2.5 \)
- For the fourth pair: \( \frac{40}{16} = 2.5 \)
- For the fifth pair: \( \frac{50}{20} = 2.5 \)

Since the ratio is constant (2.5), the quantities are proportional, and the constant of proportionality is 2.5.

Final Answer:

- Table 1: Constant of proportionality = 1.4
- Table 2: Constant of proportionality = 2
- Table 3: Constant of proportionality = 2.5

\[
\boxed{1.4, 2, 2.5}
\]