Answer: Each person has 2 legs and each dog has 4 legs. So, the total number of legs is 2X + 4Y. We know that the total number of legs is 38. Therefore, we can write the equation:
2X + 4Y = 38
To solve for X and Y, we need another equation. We know that the total number of people and dogs in the park is X + Y. But we don't know the total number of people and dogs, so we can't use this equation directly. However, we do know that X and Y are both non-negative integers (since you can't have a negative number of people or dogs). So, we can try different values of X and Y until we find a solution that satisfies both equations.
Let's start by trying X = 1 and Y = 0. Plugging these values into the first equation, we get:
2(1) + 4(0) = 2
This is not equal to 38, so this is not the solution. Let's try X = 0 and Y = 1:
2(0) + 4(1) = 4
This is also not equal to 38. Let's keep trying different values of X and Y:
X = 1, Y = 1: 2(1) + 4(1) = 6
X = 2, Y = 1: 2(2) + 4(1) = 10
X = 3, Y = 1: 2(3) + 4(1) = 14
X = 4, Y = 1: 2(4) + 4(1) = 18
X = 5, Y = 1: 2(5) + 4(1) = 22
X = 6, Y = 1: 2(6) + 4(1) = 26
X = 7, Y = 1: 2(7) + 4(1) = 30
X = 8, Y = 1: 2(8) + 4(1) = 34
X = 9, Y = 1: 2(9) + 4(1) = 38
We have found a solution! When there are 9 people and 1 dog in the park, there are a total of 38 legs.