Using Tables to Compare Ratios - Free Printable

Let's analyze the problem based on the image you've provided. It shows two recipes — Anna’s recipe and Bailey’s recipe — for mixing concentrate and water to make a drink. The goal is likely to compare the two recipes and determine which one produces a stronger or more diluted drink, or perhaps to find a common mixture or ratio.

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🔍 Step 1: Understand the Tables

#### ✔ Anna's Recipe:
- Ratio of concentrate to water:
Initial amounts: 2 cups concentrate : 3 cups water
So, the ratio is 2:3

The table shows multiples of this ratio:

| Multiply by | Concentrate (c) | Water (c) |
|-------------|------------------|-----------|
| ×2 | 4 | 6 |
| ×3 | 6 | 9 |
| ×4 | 8 | 12 |
| ×5 | 10 | 15 |

So, each time, both ingredients are multiplied by the same factor.

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#### ✔ Bailey's Recipe:
- Initial amounts: 3 cups concentrate : 5 cups water
So, the ratio is 3:5

Table shows multiples:

| Multiply by | Concentrate (c) | Water (c) |
|-------------|------------------|-----------|
| ×2 | 6 | 10 |
| ×3 | 9 | 15 |
| ×4 | 12 | 20 |
| ×5 | 15 | 25 |

Again, both ingredients scaled up proportionally.

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🔍 Step 2: Identify the Circled Values

- In Anna's recipe, the circled values are:
- Concentrate: 10 c
- Water: 15 c
→ This corresponds to ×5 of her original recipe.

- In Bailey's recipe, the circled values are:
- Concentrate: 9 c
- Water: 15 c
→ This corresponds to ×3 of her original recipe.

So both recipes have 15 cups of water, but different amounts of concentrate:
- Anna uses 10 cups concentrate with 15 cups water.
- Bailey uses 9 cups concentrate with 15 cups water.

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🔍 Step 3: Compare the Strength of the Mixes

We can compare the concentration (amount of concentrate per cup of water), or the ratio of concentrate to total liquid.

#### Option 1: Concentration (concentrate / water)

- Anna: $ \frac{10}{15} = \frac{2}{3} \approx 0.67 $
- Bailey: $ \frac{9}{15} = \frac{3}{5} = 0.6 $

So Anna’s mix has a higher concentration of concentrate.

#### Option 2: Ratio of concentrate to total liquid

- Anna: $ \frac{10}{10+15} = \frac{10}{25} = 0.4 $
- Bailey: $ \frac{9}{9+15} = \frac{9}{24} = 0.375 $

Again, Anna’s drink is stronger.

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✔ Final Answer & Explanation

> Anna's recipe makes a stronger drink than Bailey's when comparing equal amounts of water (15 cups).
> - With 15 cups of water, Anna uses 10 cups concentrate, while Bailey uses only 9 cups.
> - Therefore, Anna’s mixture has a higher concentration of concentrate.

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🎯 Conclusion

The circled values highlight a comparison at 15 cups of water:
- Anna: 10 c concentrate
- Bailey: 9 c concentrate

Since Anna uses more concentrate for the same amount of water, her recipe is stronger.

✔ Answer: Anna’s recipe results in a stronger drink than Bailey’s.