Final answer:
To find the number of dogs (X) and birds at the shelter, set up a system of equations based on the given information. Solve the system of equations to find the values of X and Y. The answer is option d. X = 10 dogs, Y = 8 birds.
Step-by-step explanation:
To find the number of dogs (X) and birds at the shelter, we can set up a system of equations based on the given information. Let's say there are X dogs and Y birds.
Each dog has 4 feet and each bird has 2 feet. Since there are a total of 18 animals and a total of 66 feet, we can write the equations:
X + Y = 18 (equation 1)
4X + 2Y = 66 (equation 2)
We now have a system of linear equations. We can solve this system by using the substitution or elimination method. Let's use the elimination method.
Multiply equation 1 by 2 to make the coefficients of Y the same in both equations:
2X + 2Y = 36 (equation 3)
Subtract equation 3 from equation 2 to eliminate Y:
(4X + 2Y) - (2X + 2Y) = 66 - 36
2X = 30
Divide both sides by 2: X = 15
Substitute X = 15 back into equation 1 to find Y: 15 + Y = 18
Subtract 15 from both sides: Y = 3
Therefore, there are 15 dogs and 3 birds at the shelter. The answer is option d. X = 10 dogs, Y = 8 birds.