Solving the Puzzle of Farmer Brown's Ducks and Cows

In the world of high school mathematics, word problems often present intriguing challenges that require both logical thinking and mathematical skills. One such problem that has been a staple in many classrooms is the case of Farmer Brown and his animals.

The scenario is as follows: Farmer Brown had a farm with both ducks and cows. One day, he noticed that the animals had a total of 12 heads and 44 feet. The question is: How many of the animals were cows?

To solve this problem, we need to understand the key information provided and set up a system of equations to find the number of cows.

Given information:

• The total number of animals is 12.
• The total number of feet is 44.

Let's represent the number of ducks as "d" and the number of cows as "c".

We know that the total number of heads is 12, and each animal has one head, so we can write the first equation: d + c = 12

Next, we know that ducks have 2 feet each, and cows have 4 feet each. The total number of feet is 44, so we can write the second equation: 2d + 4c = 44

Now, we have a system of two equations with two unknowns (d and c): d + c = 12 2d + 4c = 44

To solve this system, we can use various methods, such as substitution or elimination. Let's use the elimination method.

Step 1: Multiply the first equation by 2 to eliminate the variable "d". 2d + 2c = 24

Step 2: Subtract the first equation from the second equation to eliminate the variable "d". 2d + 4c = 44

2d + 2c = 24

2c = 20

Step 3: Solve for the variable "c" (the number of cows). c = 20 / 2 c = 10

Therefore, the number of cows on Farmer Brown's farm is 10.

By setting up the system of equations and solving them, we have successfully determined the number of cows on Farmer Brown's farm. This problem illustrates the importance of understanding the given information, translating it into mathematical equations, and applying logical reasoning to find the solution.