To make orange fizz, Noah mixes 4 scoops of powder with 6 cups of water. Andre mixes 5 scoops of powder with 8 cups of water.
1. Create a double number line or a table that shows different amounts of powder and water that taste the same as Noah’s mixture.
2. Create a double number line or a table that shows different amounts of powder and water that taste the same as Andre’s mixture.
3. How do their two mixtures compare in taste? Explain your reasoning.

### 1. Double Number Line or Table for Noah's Mixture

Noah's mixture uses 4 scoops of powder for every 6 cups of water. We can find equivalent ratios by scaling up or down, keeping the ratio of scoops to water the same (4:6). Simplifying, the ratio can be reduced to 2:3.

**Table for Noah's Mixture:**
| Scoops of Powder | Cups of Water |
|------------------|---------------|
| 2                | 3             |
| 4                | 6             |
| 6                | 9             |
| 8                | 12            |
| 10               | 15            |

This shows the different amounts that will keep the mixture tasting the same as Noah’s original recipe.

### 2. Double Number Line or Table for Andre's Mixture

Andre's mixture uses 5 scoops of powder for every 8 cups of water. We'll again find equivalent ratios by scaling this up or down while maintaining the ratio (5:8).

**Table for Andre's Mixture:**
| Scoops of Powder | Cups of Water |
|------------------|---------------|
| 5                | 8             |
| 10               | 16            |
| 15               | 24            |
| 20               | 32            |
| 25               | 40            |

These are the equivalent amounts that will keep Andre’s mixture tasting the same.

### 3. Comparison of Their Mixtures

To compare their mixtures, let's look at the simplified ratios:

- Noah's ratio (simplified): 2 scoops of powder per 3 cups of water (2:3).
- Andre's ratio: 5 scoops of powder per 8 cups of water (5:8).

If we express both ratios in terms of scoops of powder per cup of water:

- Noah’s mixture: \( \frac{2}{3} \) scoops per cup of water ≈ 0.67 scoops per cup.
- Andre’s mixture: \( \frac{5}{8} \) scoops per cup of water ≈ 0.625 scoops per cup.

Since Noah's mixture has a higher concentration of powder (0.67 scoops per cup) compared to Andre's (0.625 scoops per cup), Noah's mixture will taste slightly stronger or more concentrated than Andre's mixture.

### Do you want more details or have any questions?

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Here are 5 related questions:
1. If Noah used 10 cups of water, how many scoops of powder would he need to keep the same taste?
2. How many cups of water would Andre need to mix with 15 scoops of powder to maintain his mixture's taste?
3. If they combined their mixtures, what would be the overall ratio of powder to water?
4. Can you create a mixture that lies exactly between the concentrations of Noah's and Andre’s mixtures?
5. How many cups of water would you need to add to Noah’s mixture to match Andre’s concentration?

**Tip:** To compare mixtures easily, it's often useful to express them as a ratio of "amount per 1 unit."

To make orange fizz, Noah mixes 4 scoops of powder with 6 cups of water. Andre mixes 5 scoops of powder with 8 cups of water. 1. Create a double number line or a table that shows different amounts of powder and water that taste the same as Noah’s mixture. 2. Create a double number line or a table that shows different amounts of powder and water that taste the same as Andre’s mixture. 3. How do their two mixtures compare in taste? Explain your reasoning.

Explore the comparison of two drink mixtures: Noah's using a 4:6 ratio of powder to water, and Andre's using a 5:8 ratio. Learn how to create tables showing equivalent amounts and analyze which mixture is more concentrated using ratio and proportion concepts. Suitable for Grades 6-8.

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