A mixed fruit juice carton has apple and pineapple juice in the ratio 4:9. If the quantity of the apple juice is 4.8 L, find the quantity of juice in the carton and also the amount of pineapple juice in the carton.

Answer

To solve the problem step by step, we will follow the given information about the ratio of apple juice to pineapple juice and the quantity of apple juice.

### Step 1: Understand the Ratio
The ratio of apple juice to pineapple juice is given as 4:9. This means for every 4 parts of apple juice, there are 9 parts of pineapple juice.

### Step 2: Set Up the Equation
Let the common multiple be \( x \). Therefore, we can express the quantities of apple juice and pineapple juice as:
- Apple juice = \( 4x \)
- Pineapple juice = \( 9x \)

### Step 3: Use the Given Quantity of Apple Juice
We know that the quantity of apple juice is 4.8 L. So, we can set up the equation:
\[ 4x = 4.8 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides of the equation by 4:
\[ x = \frac{4.8}{4} \]
Calculating this gives:
\[ x = 1.2 \]

### Step 5: Calculate the Quantity of Pineapple Juice
Now that we have \( x \), we can find the quantity of pineapple juice:
\[ \text{Pineapple juice} = 9x = 9 \times 1.2 \]
Calculating this gives:
\[ \text{Pineapple juice} = 10.8 \text{ L} \]

### Step 6: Calculate the Total Quantity of Juice
Finally, we can find the total quantity of juice in the carton by adding the quantities of apple juice and pineapple juice:
\[ \text{Total juice} = \text{Apple juice} + \text{Pineapple juice} \]
Substituting the values we have:
\[ \text{Total juice} = 4.8 + 10.8 \]
Calculating this gives:
\[ \text{Total juice} = 15.6 \text{ L} \]

### Final Answers
- Quantity of pineapple juice: 10.8 L
- Total quantity of juice in the carton: 15.6 L

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