Question

There are apples and oranges in a basket that can carry a maximum of 50 fruits. Some fruits are rotten and some are good. The number of rotten apples is twice the number of good apples. The number of good oranges is twice the number of rotten oranges. The number of oranges is thrice the number of apples. If there are more than 40 fruits in the basket, what is the total number of apples and oranges?

Answer 1

Correct Answer: 48

Let \(a\) represent the number of apples and \(o\) the number of oranges. According to the problem: 

1. The total number of apples and oranges equals 3 times the apples: \(o = 3a\).

2. Let \( x \) be the number of good apples, then the rotten apples are \( 2x \).

3. Let \( y \) be the number of rotten oranges, then good oranges are \( 2y \).

4. Total fruit condition equation: \( x + 2x + 2y + y = 3x + 3y \).

5. The basket can carry a maximum of 50 fruits, and it contains more than 40 fruits.

We want \( a + o > 40 \) and \( a + o \leq 50 \).

Since \( a + o = 4a \) (substituting \( o = 3a \)), the constraint becomes:

\(40 < 4a \leq 50\).

Solving, divide the inequality by 4:

\(10 < a \leq 12.5\).

Since \( a \) must be an integer, possible values are \( a = 11 \) or \( a = 12 \).

Let's check:

• For \( a = 11 \), \( o = 3 \times 11 = 33 \), total = 44. This satisfies \( 40 < 44 \leq 50 \).
• For \( a = 12 \), \( o = 3 \times 12 = 36 \), total = 48. This satisfies \( 40 < 48 \leq 50 \).

Therefore, the total number of apples and oranges is 48, which fits the expected range of 48 to 48.