Compare ratio relationships worksheet - Free Printable

Let's solve each problem step by step and explain the reasoning.

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Problem 1: Compare Raisin-to-Cereal Ratios

Given:
- Brand A: 60 raisins in a 24-ounce box.
- Brand B: Table of data.
- Brand C: Graph of data.

We need to find which brand has the greatest ratio of raisins to ounces of cereal.

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#### Step 1: Calculate Brand A’s Ratio
$$
\text{Ratio} = \frac{\text{Raisins}}{\text{Ounces}} = \frac{60}{24} = 2.5 \text{ raisins per ounce}
$$

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#### Step 2: Analyze Brand B (from table)

| Ounces | Raisins |
|--------|---------|
| 6 | 18 |
| 12 | 36 |
| 20 | 60 |
| 24 | 72 |

Let’s calculate the ratio for each:
- $ \frac{18}{6} = 3 $
- $ \frac{36}{12} = 3 $
- $ \frac{60}{20} = 3 $
- $ \frac{72}{24} = 3 $

✔ So, Brand B has a constant ratio of 3 raisins per ounce.

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#### Step 3: Analyze Brand C (from graph)

Look at the points on the graph:

- At 10 oz → ~20 raisins → $ \frac{20}{10} = 2 $
- At 15 oz → ~30 raisins → $ \frac{30}{15} = 2 $
- At 20 oz → ~40 raisins → $ \frac{40}{20} = 2 $
- At 25 oz → ~50 raisins → $ \frac{50}{25} = 2 $

So, Brand C has a ratio of 2 raisins per ounce.

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#### Compare All Brands:
- Brand A: 2.5
- Brand B: 3.0
- Brand C: 2.0

✔ Brand B has the greatest ratio.

> ✔ Answer: Brand B has the greatest ratio of raisins to ounces of cereal.

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Problem 2: Compare Resistance to Cardio Time Ratios

We are given ratios for three people:

- Alex: 24 min resistance / 30 min cardio
- Carisa: 15 min resistance / 20 min cardio
- Manuel: 14 min resistance / 15 min cardio

We need to find who has the greatest ratio of resistance to cardio.

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#### Calculate Each Ratio:

1. Alex:
$$
\frac{24}{30} = 0.8
$$

2. Carisa:
$$
\frac{15}{20} = 0.75
$$

3. Manuel:
$$
\frac{14}{15} \approx 0.933...
$$

Now compare:
- Alex: 0.8
- Carisa: 0.75
- Manuel: ≈0.933

✔ Manuel has the highest ratio.

> ✔ Answer: Manuel has the greatest ratio of minutes spent on resistance to cardio.

*(Note: You can fill in the tables as multiples if needed, but the ratio comparison is sufficient.)*

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Problem 3: Compare Calories to Slices in Bread

Given:
- Wheat bread: 150 calories per 2 slices → $ \frac{150}{2} = 75 $ cal/slice
- White bread: Table provided
- Rye bread: Graph provided

We need to find which bread has the greatest ratio of calories to slices.

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#### Step 1: Wheat Bread
$$
\frac{150}{2} = 75 \text{ calories per slice}
$$

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#### Step 2: White Bread (from table)

| Slices | Calories |
|--------|----------|
| 2 | 160 |
| 4 | 320 |
| 6 | 480 |

Check ratios:
- $ \frac{160}{2} = 80 $
- $ \frac{320}{4} = 80 $
- $ \frac{480}{6} = 80 $

✔ Constant ratio: 80 calories per slice

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#### Step 3: Rye Bread (from graph)

Estimate points from graph:

- At 2 slices → ~150 calories → $ \frac{150}{2} = 75 $
- At 4 slices → ~250 calories → $ \frac{250}{4} = 62.5 $
- At 6 slices → ~400 calories → $ \frac{400}{6} \approx 66.67 $

Wait — this seems inconsistent. Let’s check more carefully.

But look: the point at 6 slices is at ~400 calories, so:
$$
\frac{400}{6} \approx 66.67
$$

But earlier points:
- At 2 slices: ~150 → 75
- At 4 slices: ~250 → 62.5

This suggests not a constant ratio, but we want the average ratio or perhaps assume linearity?

Actually, let's check if it's proportional.

Try finding slope between points:
- From (2,150) to (4,250): increase of 100 calories for 2 slices → 50 cal/slice? But that doesn’t match.

Wait — better to compute each point’s ratio:

- 2 slices → 150 cal → $ \frac{150}{2} = 75 $
- 4 slices → 250 cal → $ \frac{250}{4} = 62.5 $
- 6 slices → 400 cal → $ \frac{400}{6} \approx 66.67 $

But these are not consistent. However, the graph may be linear, so maybe we should find the unit rate using the trend.

But since it's not perfectly proportional, we might need to see which bread has the highest average calorie per slice.

But actually, let's re-express:

Wait — White bread has 80 cal/slice.

Wheat bread: 75 cal/slice.

Rye bread:
- The highest point is 6 slices → ~400 cal → ~66.67 cal/slice
- Even the first point is only 75 cal/slice

So maximum ratio for rye is 75 (at 2 slices), but others are lower.

So the highest ratio among all breads is white bread at 80 cal/slice.

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#### Final Comparison:

- Wheat bread: 75 cal/slice
- White bread: 80 cal/slice
- Rye bread: max 75 cal/slice (at 2 slices), less elsewhere

✔ White bread has the greatest ratio of calories to slices.

> ✔ Answer: White bread has the greatest ratio of calories to slices.

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✔ Final Answers Summary:

1. Brand B has the greatest ratio of raisins to ounces.
2. Manuel has the greatest ratio of resistance to cardio time.
3. White bread has the greatest ratio of calories to slices.

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Let me know if you'd like the filled-in tables or graphs!