Question

Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base. After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen. He also finds that the perimeter of the pen is 3 times greater than the perimeter of the doghouse.

If x represents the length of the pen and y represents the area of the doghouse, then which of the following systems of equations can be used to determine the length and width of the pen and the area of the doghouse?

Answer 1

just took the test, got 5/5, they're correct.

Explanation:

Answer 2

I believe the answer is C, as it would fit all the criteria needed to have to answer a question like it, for example: The question must include what it equals (obviously) on one side, it must also have x^2, once again, all of them do. However, there must be + 3x to account for the longer side (if x=2 and one side is 3 feet wider than the length then 4+6=10, if x=3 then 9+9=18 and so on) which C, B, and D all have. Finally, there must be an account for y, which would require subtracting y from the total area, which is only in C.