If 1 cup of milk is added to a 3-cup mixture that is `(2)/(3)` flour and `(3)/(5)` milk, what percent of the 4-cup mixture is milk?

Options

A. `80%`
B. `75%`
C. `70%`
D. `65%`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Determine the amount of milk in the initial mixture.
The initial mixture is 3 cups, where the fraction of milk is \( \frac{3}{5} \).
To find the amount of milk in the 3-cup mixture, we calculate:

\[ \text{Amount of milk} = \left(\frac{3}{5}\right) \times 3 = \frac{9}{5} \text{ cups} \]

### Step 2: Add the additional cup of milk.
We are adding 1 cup of milk to the initial amount of milk. Therefore, we calculate the total amount of milk after adding:

\[ \text{Total milk} = \frac{9}{5} + 1 = \frac{9}{5} + \frac{5}{5} = \frac{14}{5} \text{ cups} \]

### Step 3: Determine the total volume of the mixture.
After adding the 1 cup of milk to the initial 3 cups, the total volume of the mixture is:

\[ \text{Total mixture} = 3 + 1 = 4 \text{ cups} \]

### Step 4: Calculate the percentage of milk in the total mixture.
To find the percentage of milk in the 4-cup mixture, we use the formula for percentage:

\[ \text{Percentage of milk} = \left(\frac{\text{Amount of milk}}{\text{Total mixture}}\right) \times 100 \]

Substituting the values we have:

\[ \text{Percentage of milk} = \left(\frac{\frac{14}{5}}{4}\right) \times 100 \]

Calculating this gives:

\[ = \left(\frac{14}{5} \div 4\right) \times 100 = \left(\frac{14}{5} \times \frac{1}{4}\right) \times 100 = \left(\frac{14}{20}\right) \times 100 = \left(\frac{7}{10}\right) \times 100 = 70\% \]

### Final Answer:
The percentage of milk in the 4-cup mixture is **70%**.

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