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### Question 3 (Graph-based Conversion between Pints and Fluid Ounces):

#### a. Are the number of pints and the number of fluid ounces proportional?
To determine if two quantities are proportional, the ratio between them should remain constant. 

Let's check the data points from the graph:
- (3 pints, 48 fluid ounces)
- (6 pints, 96 fluid ounces)
- (9 pints, 144 fluid ounces)
- (15 pints, 240 fluid ounces)

For each pair, calculate the ratio:
\[
\text{Ratio} = \frac{\text{fluid ounces}}{\text{pints}} = \frac{48}{3} = 16, \frac{96}{6} = 16, \frac{144}{9} = 16, \frac{240}{15} = 16
\]

Since the ratio between fluid ounces and pints is constant at 16, the relationship is **proportional**.

#### b. Write an equation relating the number of fluid ounces \( z \) to the number of pints \( p \).
From the graph and the ratios calculated, we see that for every pint, there are 16 fluid ounces. Thus, the equation is:
\[
z = 16p
\]
where \( z \) is the number of fluid ounces, and \( p \) is the number of pints.

#### c. A recipe requires 11 pints of water. How many fluid ounces of water are in 11 pints of water?
Using the equation from part b \( z = 16p \), substitute \( p = 11 \):
\[
z = 16 \times 11 = 176 \, \text{fluid ounces}
\]
So, 11 pints of water is equivalent to 176 fluid ounces.

#### d. An average ice cube contains 1 fluid ounce of water. Shawn puts 64 ice cubes into an empty pitcher. When the ice cubes melt, approximately how many pints of water are in the pitcher?
Each ice cube is 1 fluid ounce, so 64 ice cubes contain:
\[
64 \, \text{fluid ounces}
\]
Since \( 16 \, \text{fluid ounces} = 1 \, \text{pint} \), divide 64 by 16:
\[
\frac{64}{16} = 4 \, \text{pints}
\]
So, there will be approximately 4 pints of water in the pitcher.

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Do you have any further questions or would you like additional explanations on any part of the solution? Here are 5 related questions for further practice:

1. If 7 pints of water were used, how many fluid ounces would that be?
2. How would you determine if two quantities are inversely proportional?
3. What happens to the fluid ounces if the number of pints triples?
4. If Shawn used only 32 ice cubes, how many pints would there be after melting?
5. What other real-world situations involve proportional relationships like this?

**Tip:** For proportional relationships, always check if the ratio between two quantities remains constant throughout the data points!

The graph shows conversions between the number of pints and the number of fluid ounces. Are the number of pints and the number of fluid ounces proportional? Write an equation relating the number of fluid ounces z to the number of pints p. A recipe requires 11 pints of water. How many fluid ounces of water are in 11 pints of water? An average ice cube contains 1 fluid ounce of water. Shawn puts 64 ice cubes into an empty pitcher. When the ice cubes melt, approximately how many pints of water are in the pitcher?

This lesson covers proportional relationships between pints and fluid ounces, unit conversions, and solving real-world math problems such as calculating the number of fluid ounces in multiple pints of water. Includes step-by-step solutions and explanations.

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