Silky Dark Chocolate is `80%` cocoa.
Rich Milk Chocolate is `50%` cocoa.
Smooth white Chocolate is `0%` cocoa.
`{:("Quantity A","Quantity B"),("Percent cocoa of a mixture of 3","Percent cocoa of a mixture of 2"),("parts Silky Dark Chocolate and","parts Rich Milk Chocolate and 1"),("1 part Smooth White Chocolate","part Silky Dark Chocolate"):}`

Options

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the infromation given.

Answer

To solve the problem, we need to calculate the percentage of cocoa in two different mixtures: Quantity A and Quantity B.

### Step-by-Step Solution:

**Step 1: Calculate Quantity A**
- Quantity A consists of 3 parts Silky Dark Chocolate and 1 part Smooth White Chocolate.
- The total parts in Quantity A = 3 + 1 = 4 parts.
- Since we need to find the percentage of cocoa, we will assume a total mixture of 12 units. Therefore, each part = 12 / 4 = 3 units.

**Step 2: Determine the cocoa content in Quantity A**
- Silky Dark Chocolate contains 80% cocoa. Thus, the cocoa from 3 parts of Silky Dark Chocolate:
\[ \text{Cocoa from Silky Dark Chocolate} = 3 \text{ parts} \times 3 \text{ units/part} \times 0.80 = 7.2 \text{ units of cocoa} \]
- Smooth White Chocolate contains 0% cocoa, so:
\[ \text{Cocoa from Smooth White Chocolate} = 1 \text{ part} \times 3 \text{ units/part} \times 0 = 0 \text{ units of cocoa} \]
- Therefore, the total cocoa in Quantity A:
\[ \text{Total cocoa in Quantity A} = 7.2 + 0 = 7.2 \text{ units of cocoa} \]

**Step 3: Calculate Quantity B**
- Quantity B consists of 2 parts Rich Milk Chocolate and 1 part Silky Dark Chocolate.
- The total parts in Quantity B = 2 + 1 = 3 parts.
- Again, we assume a total mixture of 12 units. Therefore, each part = 12 / 3 = 4 units.

**Step 4: Determine the cocoa content in Quantity B**
- Rich Milk Chocolate contains 50% cocoa. Thus, the cocoa from 2 parts of Rich Milk Chocolate:
\[ \text{Cocoa from Rich Milk Chocolate} = 2 \text{ parts} \times 4 \text{ units/part} \times 0.50 = 4 \text{ units of cocoa} \]
- Silky Dark Chocolate contains 80% cocoa, so:
\[ \text{Cocoa from Silky Dark Chocolate} = 1 \text{ part} \times 4 \text{ units/part} \times 0.80 = 3.2 \text{ units of cocoa} \]
- Therefore, the total cocoa in Quantity B:
\[ \text{Total cocoa in Quantity B} = 4 + 3.2 = 7.2 \text{ units of cocoa} \]

**Step 5: Compare Quantity A and Quantity B**
- Quantity A has 7.2 units of cocoa and Quantity B also has 7.2 units of cocoa.
- Therefore, both quantities are equal.

### Conclusion:
- Quantity A = Quantity B = 7.2 units of cocoa.
- The answer is that both quantities are equal.

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