The Fruit Basket Puzzle

 

The Fruit Basket Puzzle

Question :

You have a basket filled with only apples, bananas, and oranges. There are a total of 20 pieces of fruit in the basket. The number of apples is equal to the number of bananas plus the number of oranges. Additionally, the number of bananas is equal to the number of oranges.

Given this information, can you determine how many apples, bananas, and oranges are in the basket?

Solution:

Let's denote the number of apples as $𝐴$, the number of bananas as $𝐵$, and the number of oranges as $𝑂$.

1. The total number of fruit is 20: So, we have the equation $𝐴+𝐵+𝑂=20$.

2. The number of apples is equal to the number of bananas plus the number of oranges: This gives us the equation $𝐴=𝐵+𝑂$.

3. The number of bananas is equal to the number of oranges: This gives us the equation $𝐵=𝑂$.

We can use these equations to solve for the values of $𝐴$, $𝐵$, and $𝑂$.

From equation 3, we know that $𝐵=𝑂$. So, we can substitute $𝑂$ for $𝐵$ in equations 1 and 2.

Substituting $𝑂$ for $𝐵$ in equation 1: $𝐴+𝐵+𝐵=20$ $𝐴+2𝐵=20$

Substituting $𝑂$ for $𝐵$ in equation 2: $𝐴=𝐵+𝑂$ $𝐴=𝐵+𝐵$ $𝐴=2𝐵$

Now, we have a system of equations:

$𝐴+2𝐵=20$ $𝐴=2𝐵$

We can solve this system of equations to find the values of $𝐴$ and $𝐵$.

From equation 2, we can see that $𝐴=2𝐵$. So, if we substitute $2𝐵$ for $𝐴$ in equation 1, we get:

$2𝐵+2𝐵=20$ $4𝐵=20$ $𝐵=5$

Now that we know $𝐵=5$, we can find $𝐴$ using equation 2:

$𝐴=2𝐵$ $𝐴=2\times 5$ $𝐴=10$

And since $𝐵=𝑂$, $𝑂=5$.

So, the number of apples, bananas, and oranges in the basket are:

• Apples: 10
• Bananas: 5
• Oranges: 5