Exchange Ratio Between Mangoes and Chicos: A Mathematical Analysis

The problem presented is a straightforward yet interesting comparison between the cost of mangoes and chicos, two fruits that are often compared due to their similarity in pricing or cost per weight. In this analysis, we will explore the relationship between the quantities of these two fruits, focusing on the exchange ratio and solving for the number of kilograms of mangoes that would cost the same as a given amount of chicos.

Let's break down the problem: If 3 kg of mangoes cost as much as 5 kg of chicos, how many kilograms of mangoes would cost the same as 60 kg of chicos?

Step-by-Step Solution

Given the ratio of the cost of mangoes to chicos, we can set up the following relationship:

3 kg of mangoes 5 kg of chicos

This ratio can be written as:

3 kg mangoes / 5 kg chicos 1

Therefore, for every 5 kg of chicos, the equivalent cost would be 3 kg of mangoes.

Calculating the Exchange Ratio for 60 kg of Chicos

To find out how many kilograms of mangoes would cost the same as 60 kg of chicos, we use the given ratio:

First, determine how many times 5 kg fits into 60 kg of chicos:

60 kg / 5 kg 12

Next, multiply this by the corresponding amount of mangoes (3 kg):

12 × 3 kg 36 kg

Hence, 60 kg of chicos would cost the same as 36 kg of mangoes.

Verifying the Solution Using Proportions

Using proportions, we can further validate our solution:

3 kg of mangoes / 5 kg of chicos x kg of mangoes / 60 kg of chicos

Solving for x (the amount of mangoes that would cost the same as 60 kg of chicos), we get:

5x 3 × 60

x (3 × 60) / 5

x 180 / 5

x 36

Alternative Method Using Total Quantity

We can also approach this by considering the total quantity:

The ratio given is 3 kg of mangoes to 5 kg of chicos:

3 kg mangoes / 5 kg chicos 60 kg chicos / x kg mangoes

Let x be the total quantity of fruits combined (both mangoes and chicos). Given that 5 kg of chicos is part of this total, we can set up the equation:

5/8 x 60 kg

x (60 × 8) / 5

x 480 / 5

x 96 kg

Therefore, the total quantity of fruits is 96 kg. Subtracting the 60 kg of chicos, we get:

Quantity of mangoes 96 kg - 60 kg 36 kg

This again confirms that 60 kg of chicos is equivalent to 36 kg of mangoes.

Conclusion

In conclusion, the problem of exchanging mangoes for chicos based on their cost can be straightforwardly solved using ratios and proportions. The crux of the solution lies in understanding the exchange rate, which in this case, means that 60 kg of chicos is equivalent to 36 kg of mangoes. This analysis demonstrates the power of mathematical thinking in solving real-world problems involving cost comparisons and exchanges.