A mixed fruit juice carton has orange and grape juice in the ratio 2:7. If the quantity of the orange juice is 2.4 litres, find the quantity of juice in the carton and also the quantity of grape juice in the carton.

Answer

To solve the problem step by step, let's follow the instructions given in the question.

### Step 1: Understand the Ratio
The ratio of orange juice to grape juice is given as 2:7. This means for every 2 parts of orange juice, there are 7 parts of grape juice.

### Step 2: Define Variables
Let the common multiple be \( x \). Therefore, the quantities of orange and grape juice can be expressed as:
- Orange juice = \( 2x \)
- Grape juice = \( 7x \)

### Step 3: Set Up the Equation
We know from the problem that the quantity of orange juice is 2.4 litres. Thus, we can set up the equation:
\[ 2x = 2.4 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides of the equation by 2:
\[ x = \frac{2.4}{2} = 1.2 \]

### Step 5: Calculate the Quantity of Grape Juice
Now that we have \( x \), we can find the quantity of grape juice:
\[ \text{Grape juice} = 7x = 7 \times 1.2 = 8.4 \text{ litres} \]

### Step 6: Calculate the Total Quantity of Juice
The total quantity of juice in the carton is the sum of the quantities of orange juice and grape juice:
\[ \text{Total juice} = \text{Orange juice} + \text{Grape juice} = 2.4 + 8.4 = 10.8 \text{ litres} \]

### Final Answers
- Quantity of grape juice: **8.4 litres**
- Total quantity of juice in the carton: **10.8 litres**

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