Question
A fruit fuice blend is made by mixing the juice of oranges and apples in the ratio \( 7: 5 \). If 168 littes of orange |uice is used, how many litres of apple juice must be used?
Ask by Montgomery Pollard. in South Africa
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
120 litres of apple juice must be used.
Solution
To determine how many litres of apple juice are needed, we can use the given ratio of orange juice to apple juice, which is \( 7:5 \).
1. **Understanding the Ratio:**
- **Orange Juice:** 7 parts
- **Apple Juice:** 5 parts
2. **Given:**
- **Amount of Orange Juice:** 168 litres
3. **Set Up the Proportion:**
\[
\frac{\text{Orange Juice}}{\text{Apple Juice}} = \frac{7}{5} = \frac{168}{x}
\]
where \( x \) is the amount of apple juice needed.
4. **Solve for \( x \):**
\[
\frac{7}{5} = \frac{168}{x}
\]
Cross-multiply to solve for \( x \):
\[
7x = 5 \times 168
\]
\[
7x = 840
\]
\[
x = \frac{840}{7} = 120
\]
5. **Conclusion:**
- **Apple Juice Required:** 120 litres
**Answer:** 120 litres of apple juice must be used.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To find the amount of apple juice needed, we first establish the ratio of orange juice to apple juice, which is \(7:5\). This means for every 7 parts of orange juice, there are 5 parts of apple juice. Since we have 168 litres of orange juice, we can set up a proportion. If 7 parts represent 168 litres, we can find the value of one part: \[ 1 \text{ part} = \frac{168 \text{ litres}}{7} = 24 \text{ litres} \] Now, we calculate the apple juice (which is 5 parts): \[ 5 \text{ parts of apple juice} = 5 \times 24 \text{ litres} = 120 \text{ litres} \] Thus, you need 120 litres of apple juice to mix with the orange juice.
