Question
Suppose that Hare has apples to oranges in the ratio of 2:1 and oranges to bananas in the ratio of 2:3. If Hare has 15 bananas, how many apples does he have?
Answers
GPT-4o mini
To solve the problem, we start by determining the relationships between the quantities of apples, oranges, and bananas.
1. Let the number of apples be \( A \), the number of oranges be \( O \), and the number of bananas be \( B \).
2. The first given ratio is that the number of apples to the number of oranges is \( 2:1 \), which can be expressed as:
\[
A = 2O
\]
3. The second given ratio is that the number of oranges to the number of bananas is \( 2:3 \), expressed as:
\[
O = \frac{2}{3}B
\]
4. We are given that \( B = 15 \) (i.e., Hare has 15 bananas).
5. First, we find the number of oranges \( O \):
\[
O = \frac{2}{3}B = \frac{2}{3} \times 15 = 10
\]
6. Now that we have \( O = 10 \), we can find the number of apples \( A \) using the first ratio \( A = 2O \):
\[
A = 2O = 2 \times 10 = 20
\]
Therefore, Hare has \(\boxed{20}\) apples.
1. Let the number of apples be \( A \), the number of oranges be \( O \), and the number of bananas be \( B \).
2. The first given ratio is that the number of apples to the number of oranges is \( 2:1 \), which can be expressed as:
\[
A = 2O
\]
3. The second given ratio is that the number of oranges to the number of bananas is \( 2:3 \), expressed as:
\[
O = \frac{2}{3}B
\]
4. We are given that \( B = 15 \) (i.e., Hare has 15 bananas).
5. First, we find the number of oranges \( O \):
\[
O = \frac{2}{3}B = \frac{2}{3} \times 15 = 10
\]
6. Now that we have \( O = 10 \), we can find the number of apples \( A \) using the first ratio \( A = 2O \):
\[
A = 2O = 2 \times 10 = 20
\]
Therefore, Hare has \(\boxed{20}\) apples.