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A salad dressing requires oil, vinegar, and water in the ratio 2 : 1 : 3. If Oliver has 1 cup of oil, 1/3 cup of vinegar, and 2 cups of water, what is the maximum number of cups of dressing that he can mix?
- a)1
- b)2
- c)3
- d)4
- e)5
Correct answer is option 'B'. Can you explain this answer?
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A salad dressing requires oil, vinegar, and water in the ratio 2 : 1 :...
Understanding the Ratio
The salad dressing requires oil, vinegar, and water in the ratio of 2 : 1 : 3. This means for every 2 parts of oil, there is 1 part of vinegar and 3 parts of water.
Calculating Total Parts
To find the total parts in the mixture:
- Oil: 2 parts
- Vinegar: 1 part
- Water: 3 parts
Total = 2 + 1 + 3 = 6 parts
Determining Individual Requirements
To make 1 full batch of dressing (6 parts), the quantities needed are:
- Oil: \( \frac{2}{6} \) of total mixture
- Vinegar: \( \frac{1}{6} \) of total mixture
- Water: \( \frac{3}{6} \) of total mixture
Available Ingredients
Oliver has:
- 1 cup of oil
- \( \frac{1}{3} \) cup of vinegar
- 2 cups of water
Finding Maximum Possible Batches
Now we determine how many batches can be made from each ingredient:
1. **Oil**:
- Total batches from oil = \( \frac{1 \text{ cup}}{\frac{2}{6} \text{ cups/batch}} = \frac{1 \times 6}{2} = 3 \) batches
2. **Vinegar**:
- Total batches from vinegar = \( \frac{\frac{1}{3} \text{ cup}}{\frac{1}{6} \text{ cups/batch}} = \frac{1/3 \times 6}{1} = 2 \) batches
3. **Water**:
- Total batches from water = \( \frac{2 \text{ cups}}{\frac{3}{6} \text{ cups/batch}} = \frac{2 \times 6}{3} = 4 \) batches
Final Calculation
The limiting ingredient is vinegar, allowing for a maximum of 2 batches. Thus, the maximum number of cups of dressing that Oliver can mix is:
Answer: 2 cups
The salad dressing requires oil, vinegar, and water in the ratio of 2 : 1 : 3. This means for every 2 parts of oil, there is 1 part of vinegar and 3 parts of water.
Calculating Total Parts
To find the total parts in the mixture:
- Oil: 2 parts
- Vinegar: 1 part
- Water: 3 parts
Total = 2 + 1 + 3 = 6 parts
Determining Individual Requirements
To make 1 full batch of dressing (6 parts), the quantities needed are:
- Oil: \( \frac{2}{6} \) of total mixture
- Vinegar: \( \frac{1}{6} \) of total mixture
- Water: \( \frac{3}{6} \) of total mixture
Available Ingredients
Oliver has:
- 1 cup of oil
- \( \frac{1}{3} \) cup of vinegar
- 2 cups of water
Finding Maximum Possible Batches
Now we determine how many batches can be made from each ingredient:
1. **Oil**:
- Total batches from oil = \( \frac{1 \text{ cup}}{\frac{2}{6} \text{ cups/batch}} = \frac{1 \times 6}{2} = 3 \) batches
2. **Vinegar**:
- Total batches from vinegar = \( \frac{\frac{1}{3} \text{ cup}}{\frac{1}{6} \text{ cups/batch}} = \frac{1/3 \times 6}{1} = 2 \) batches
3. **Water**:
- Total batches from water = \( \frac{2 \text{ cups}}{\frac{3}{6} \text{ cups/batch}} = \frac{2 \times 6}{3} = 4 \) batches
Final Calculation
The limiting ingredient is vinegar, allowing for a maximum of 2 batches. Thus, the maximum number of cups of dressing that Oliver can mix is:
Answer: 2 cups
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A salad dressing requires oil, vinegar, and water in the ratio 2 : 1 : 3. If Oliver has 1 cup of oil, 1/3 cup of vinegar, and 2 cups of water, what is the maximum number of cups of dressing that he can mix?a)1b)2c)3d)4e)5Correct answer is option 'B'. Can you explain this answer?
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