A small company uses oranges and apples to make a juice blend. The ratio of oranges to apples (in volume) required to make the blend is 5:2. The person making the blend has 27 litres of orange concentrates and 9 litres of apples con- centrate. What is the maximum amount juice blend he can make? A. 18 B. 22.5 C. 31.5 D. 36
A small company uses oranges and apples to make a juice blend. The ratio of oranges to apples (in volume) required to make the blend is 5:2. The person making the blend has 27 litres of orange concentrates and 9 litres of apples con- centrate. What is the maximum amount juice blend he can make? A. 18 B. 22.5 C. 31.5 D. 36
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Juice Blend Ratio Problem**
A small company uses oranges and apples to make a juice blend. The ratio of oranges to apples (in volume) required to make the blend is 5:2. The person making the blend has 27 litres of orange concentrates and 9 litres of apple concentrate.
**Question:**
What is the maximum amount of juice blend he can make?
**Answer Choices:**
A. 18
B. 22.5
C. 31.5
D. 36
**Solution Explanation:**
To solve this problem, we need to determine how many complete batches of the juice blend can be made with the available concentrates, based on the given ratio of 5:2.
1. **Calculate the amount of each ingredient per batch:**
- According to the ratio 5:2, for every 5 parts of orange concentrate, 2 parts of apple concentrate are needed.
2. **Determine the maximum number of batches using the orange concentrate:**
- Since there are 27 litres of orange concentrate, we divide by 5 (since each batch needs 5 parts):
\[
\frac{27 \text{ litres}}{5} = 5.4 \text{ batches}
\]
3. **Determine the maximum number of batches using the apple concentrate:**
- Since there are 9 litres of apple concentrate, we divide by 2 (since each batch needs 2 parts):
\[
\frac{9 \text{ litres}}{2} = 4.5 \text{ batches}
\]
4. **Identify the limiting factor:**
- The minimum of these two values is 4.5 batches, meaning the apple concentrate is the limiting factor. Therefore, only 4.5 batches can be produced.
5. **Calculate the total amount of juice blend:**
- Each batch consists of 5 parts of orange + 2 parts of apple = 7 parts total.
- For 4.5 batches:
\[
4.5 \text{ batches} \times 7 \text{ parts per batch} = 31.5 \text{ parts in total}
\]
Hence, the maximum amount of juice blend that can be made is 31.5 litres.
**Correct Answer:**
C. 31.5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa59c8a62-6d27-4c14-9dc5-c4241c4a7fe0%2Ffdb41fcb-baa9-46c6-ab9d-8e097d698fe0%2Fxpdojll_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Juice Blend Ratio Problem**
A small company uses oranges and apples to make a juice blend. The ratio of oranges to apples (in volume) required to make the blend is 5:2. The person making the blend has 27 litres of orange concentrates and 9 litres of apple concentrate.
**Question:**
What is the maximum amount of juice blend he can make?
**Answer Choices:**
A. 18
B. 22.5
C. 31.5
D. 36
**Solution Explanation:**
To solve this problem, we need to determine how many complete batches of the juice blend can be made with the available concentrates, based on the given ratio of 5:2.
1. **Calculate the amount of each ingredient per batch:**
- According to the ratio 5:2, for every 5 parts of orange concentrate, 2 parts of apple concentrate are needed.
2. **Determine the maximum number of batches using the orange concentrate:**
- Since there are 27 litres of orange concentrate, we divide by 5 (since each batch needs 5 parts):
\[
\frac{27 \text{ litres}}{5} = 5.4 \text{ batches}
\]
3. **Determine the maximum number of batches using the apple concentrate:**
- Since there are 9 litres of apple concentrate, we divide by 2 (since each batch needs 2 parts):
\[
\frac{9 \text{ litres}}{2} = 4.5 \text{ batches}
\]
4. **Identify the limiting factor:**
- The minimum of these two values is 4.5 batches, meaning the apple concentrate is the limiting factor. Therefore, only 4.5 batches can be produced.
5. **Calculate the total amount of juice blend:**
- Each batch consists of 5 parts of orange + 2 parts of apple = 7 parts total.
- For 4.5 batches:
\[
4.5 \text{ batches} \times 7 \text{ parts per batch} = 31.5 \text{ parts in total}
\]
Hence, the maximum amount of juice blend that can be made is 31.5 litres.
**Correct Answer:**
C. 31.5
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