Question

A farmer notes that in a field full of cows and ducks there are 35 heads and 92 feet. how many of each animal are there?

a) 21 cows and 14 ducks
b) 23 cows and 12 ducks
c) 25 cows and 10 ducks
d) 27 cows and 8 ducks

Answer 1

To solve the problem, we set up simultaneous equations with C representing cows and D representing ducks. We find that there are 11 cows and 24 ducks, a solution which does not match the provided options.

Step-by-step explanation:

The question is a classic example of a simultaneous equation problem in mathematics, where we need to find out the number of cows and ducks in a field given the total number of animals' heads and feet. Since each cow has 1 head and 4 feet, and each duck has 1 head and 2 feet, we can set up the following two equations based on the given information:

• Number of heads (cows + ducks) = 35
• Total feet (4 * cows + 2 * ducks) = 92

Let's denote the number of cows as C and the number of ducks as D. Therefore, we have the equations:

1. C + D = 35
2. 4C + 2D = 92

We can solve these equations by multiplying the first equation by 2 and subtracting it from the second equation to eliminate the variable D:

1. 2C + 2D = 70 (multiplying the first equation by 2)
2. (4C + 2D) - (2C + 2D) = 92 - 70
3. 2C = 22
4. C = 11 (dividing both sides by 2)

Now we can substitute the value of C into the first equation to find D:

1. 11 + D = 35
2. D = 35 - 11
3. D = 24

Therefore, the farmer has 11 cows and 24 ducks. Please note, however, this solution does not match any of the options provided (a-d), which may indicate a mistake in the options or in the information given. If this discrepancy arose from a typo in the provided options, the correct answer based on the calculations would be 11 cows and 24 ducks. Otherwise, double-check the numbers in the question for accuracy.