ken and mark have some ducks and pigs. when asked how many ducks and pigs they had altogether mark said there is a total of 17 heads and 42 feet. I have 3 times as many ducks as pigs. yes replied ken and we both have the same number of pigs. how many ducks does ken have

If Mark has x pigs, he has 3x ducks and Ken too has x pigs . Total animals =5x=17 which is not possible.

Anonymous, Ken also has some ducks.

If Mark has x pigs, he has 3x ducks. That's 4x heads and 10x feet.

Ken has x pigs too. If Ken also has y ducks, then that's x+y heads and 4x+2y feet.

Together they have
(1) Heads: 5 x + y = 17
(2) Feet: 14 x + 2y = 42

Solve for x and y.

Let's solve the problem step by step:

Step 1: Let's assume the number of pigs as 'x'.

Step 2: As per the given information, Ken has the same number of pigs as Mark, so Ken also has 'x' pigs.

Step 3: It is mentioned that Ken has three times as many ducks as pigs, so Ken has 3x ducks.

Step 4: To find the total number of animals, we add the number of pigs and ducks together: x (pigs) + 3x (ducks) = 4x.

Step 5: It is stated that the total number of heads is 17. Since each animal has one head, the total number of animals is 17 as well.

Step 6: We can write the equation for the total number of animals: 4x = 17.

Step 7: Solving the equation, we find: x = 17 / 4 = 4.25.

Since the number of pigs cannot be a decimal, this means our assumption for 'x' is incorrect.

Hence, based on the given information, we cannot determine the exact number of ducks Ken has.

To solve this problem, we need to break it down into smaller steps to find the solution step by step.

Let's define some variables:
Let's say the number of pigs Ken has is represented by 'P'.
Since Ken and Mark have the same number of pigs, Mark also has 'P' number of pigs.
Given that you have 3 times as many ducks as pigs, Ken has 3P ducks.
Mark, on the other hand, has 17 - P heads total (which includes both pigs and ducks) because they both have the same number of pigs.
Since each duck contributes 1 head, and there are 3P ducks, then the number of heads contributed by the ducks is 3P.
So, the number of heads contributed by the pigs can be calculated by subtracting the number of duck heads from the total number of heads: 17 - 3P.
Now, let's consider the number of feet. Each duck has 2 feet, so the total number of duck feet can be calculated by multiplying the number of ducks by 2: 3P * 2 = 6P.
Each pig has 4 feet, so the number of pig feet can be calculated by multiplying the number of pigs by 4: P * 4 = 4P.
Adding up the total number of feet, we get: 6P + 4P = 10P.
Now we have two equations:
Equation 1: 17 - 3P = Total number of heads
Equation 2: 42 = 10P + Total number of feet

Let's solve these equations to find the value of P, representing the number of pigs Ken has.

From Equation 1:
17 - 3P = Total number of heads
Re-arranging the equation:
3P = 17 - Total number of heads
3P = 17 - (42 - 10P) [Substituting the value of the total number of feet from Equation 2]
Simplifying the equation:
3P = 17 - 42 + 10P
7P = -25
P = -25/7

Since the number of pigs cannot be negative, it seems there is an error or inconsistency in the given information or calculation. Please review the problem and verify the given details to find the correct solution.