Question
22. A fruit stand sells apples, bananas, and oranges at a ratio of 3:2:1. If the fruit stand sells 20 bananas, how many total pieces of fruit does the fruit stand sell? (A) 10 (B) 30 (C) 40 (D) 50 (E) 60
Ask by Bowen Smith. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The fruit stand sells a total of 60 pieces of fruit.
Solution
The ratio of apples to bananas to oranges sold at the fruit stand is **3:2:1**.
1. **Determine the common multiple (x):**
- Let \( x \) be the common multiple.
- Number of bananas = \( 2x \).
- Given that 20 bananas are sold:
\[
2x = 20 \implies x = 10
\]
2. **Calculate the total number of fruits:**
- Total parts in the ratio = \( 3 + 2 + 1 = 6 \) parts.
- Total number of fruits = \( 6x = 6 \times 10 = 60 \).
**Answer:** (E) 60
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Simplify this solution Beyond the Answer
To solve this, we first need to determine the number of bananas in relation to the ratio given. The ratio of apples to bananas to oranges is 3:2:1, which means for every 2 parts of bananas, there are 3 parts of apples and 1 part of oranges. Since the fruit stand sells 20 bananas and the banana part is 2, we can express this as follows: If 2 parts = 20 bananas, then 1 part = 20/2 = 10. Using this, we can now find the quantities for apples and oranges: - Apples = 3 parts = 3 * 10 = 30 - Bananas = 2 parts = 20 - Oranges = 1 part = 1 * 10 = 10 Adding these quantities together gives us: 30 (apples) + 20 (bananas) + 10 (oranges) = 60 total pieces of fruit. So the answer is (E) 60.
