Solving the Fruit Basket Riddle: A Simple Guide

Whether you are a student or someone who enjoys solving puzzles, the riddle of the fruit basket is a classic that challenges your mathematical reasoning. Let's break down this problem step by step to find out how many fruits are in the basket and how many of each type.

Understanding the Problem

The riddle states that ( frac{3}{5} ) of the total fruits are apples, and the remaining ( frac{2}{5} ) are oranges. It also mentions that there are 12 oranges in the basket. Our task is to find the total number of fruits and the number of apples.

Step-by-Step Solution

Method 1: Using the Total Fruits Variable

First, let's denote the total number of fruits by ( F ).

According to the problem, ( frac{2}{5} F 12 ). To find ( F ), we solve the equation: ( F 12 div frac{2}{5} ). This can be rewritten as ( F 12 times frac{5}{2} ). Calculating this, we get ( F 30 ). So, there are 30 fruits in total.

To find the number of apples:

Since ( frac{3}{5} ) of the fruits are apples, the number of apples is ( frac{3}{5} times 30 18 ).

Method 2: Using the Apples Variable

Alternatively, let ( F ) be the total number of fruits and ( A ) be the number of apples.

We are given that ( frac{3}{5} F A ). And we know that ( frac{2}{5} F 12 ). Solving for ( F ) from ( frac{2}{5} F 12 ), we get ( F 12 div frac{2}{5} 30 ). Now, substituting ( F 30 ) into ( frac{3}{5} F A ), we find that ( A 18 ).

Conclusion

Therefore, the total number of fruits in the basket is 30, consisting of 18 apples and 12 oranges.

Additional Notes

Verifying the Solution

To verify our solution, we can check that:

( 30 18 12 ) ( 18 frac{3}{5} times 30 ) ( 12 frac{2}{5} times 30 )

These checks confirm that our solution is correct.

Final Answer

The total number of fruits in the basket is 30, with 18 apples and 12 oranges.

If you enjoyed solving this riddle, you might want to try similar problems or look into more advanced mathematical problem-solving techniques.