Understanding Ratios: Calculating the Number of Animals in Mang Leoncios' Farm

Welcome to this detailed guide on how to calculate the number of animals in Mang Leoncios' farm based on the given ratios and total number of animals. Understanding and solving such problems involves a clear grasp of proportional ratios and their practical application.

Ratios and Their Calculation

The problem at hand involves identifying the number of each type of animal in Mang Leoncios' farm given a specific ratio and the total number of animals. The ratio of cows to carabaos to goats to horses is provided as 4:2:3:1. This means that for every 10 animals in the farm, 4 are cows, 2 are carabaos, 3 are goats, and 1 is a horse.

Step-by-Step Solution

Step 1: Determine the Value of One Part

The first step is to determine what one part of the ratio represents. Given that the total number of animals is 80 and the sum of the ratios is 4 2 3 110, one part of the ratio is calculated as follows:

80 animals / 10 8 animals per part

Step 2: Calculate the Number of Each Kind of Animal

For Cows (4 parts): 8 x 4 32 cows For Carabaos (2 parts): 8 x 2 16 carabaos For Goats (3 parts): 8 x 3 24 goats For Horses (1 part): 8 x 1 8 horses

Let's verify the solution by adding the number of each kind of animal:

32 (cows) 16 (carabaos) 24 (goats) 8 (horses) 80 animals

Verification of Proportionality

To ensure that the solution follows a true proportion, we can check if the product of the numbers of any two different types of animals is equal:

32 (cows) x 8 (horses) 256

16 (carabaos) x 24 (goats) 384

Since 256 ≠ 384, this indicates that the relation is not proportional in the sense of maintaining a consistent ratio between all pairs of animals, but it correctly reflects the given ratios.

Conclusion

The use of ratios in solving such problems is a fundamental concept in arithmetic and reasoning. By understanding and applying the given ratio of 4:2:3:1 to the total number of animals, we can accurately determine the number of each kind of animal in Mang Leoncios' farm. This approach can be applied to various real-world scenarios where ratios are used to distribute quantities in a proportional manner.