A certain drink is made by adding 4 parts water to 1 part drink mix. If the amount of water is doubled, and the amount of drink mix is quadrupled, what is the new mixture is drink mix?

Options

A. `33(1)/(3)%`
B. `50%`
C. `66(2)/(3)%`
D. `80%`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the initial mixture
The initial mixture consists of:
- 4 parts of water
- 1 part of drink mix

### Step 2: Calculate the new amounts after changes
According to the problem:
- The amount of water is doubled:
\[ \text{New water amount} = 2 \times 4 = 8 \text{ parts} \]
- The amount of drink mix is quadrupled:
\[ \text{New drink mix amount} = 4 \times 1 = 4 \text{ parts} \]

### Step 3: Find the total amount of the new mixture
Now, we can find the total amount of the new mixture:
\[ \text{Total mixture} = \text{New water amount} + \text{New drink mix amount} = 8 + 4 = 12 \text{ parts} \]

### Step 4: Calculate the fraction of drink mix in the new mixture
To find the fraction of the drink mix in the new mixture:
\[ \text{Fraction of drink mix} = \frac{\text{New drink mix amount}}{\text{Total mixture}} = \frac{4}{12} \]
This simplifies to:
\[ \frac{4}{12} = \frac{1}{3} \]

### Step 5: Convert the fraction to a percentage
To convert the fraction \(\frac{1}{3}\) into a percentage:
\[ \text{Percentage of drink mix} = \frac{1}{3} \times 100 = \frac{100}{3} \approx 33.33\% \]

### Final Answer
The new mixture contains approximately \(33 \frac{1}{3}\%\) of drink mix.

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