This problem involves two unknowns, thus, it can be solved using two independent equations. We first assign a variable for each real number.
Let:
x = first real number
y = second real number
Two independent equations must then be set up which will come from the problem statement. The first equation is obtained from the statement that the average of the two real numbers is 41.375. The second equation then shows that the product of the two real numbers is equal to 1668. The equations are then:
(1) (x + y)/2 = 41.375
(2) x*y = 1668
We then express the variable y in terms of x, such that, y = 1668/x. This is then applied in equation 1 in order to have only a single variable in the equation. After doing mathematical operations, x is then calculated to be 34.75. This value of x is then substituted in the second equation to obtain y. Finally, the two real numbers have been determined to be x = 34.75 and y = 48.
Given the relationship T^2 = A^3, to compare the values of the orbital periods of X and Y, it would be easier to assign values. Since the Planet Y's distance A is twice that of Planet X's distance A, this can be shown below:
For Planet X (where A = 2):
T^2 = 2^3
T = 2.828
For Planet Y (where A = 4)
T^2 = 4^3
T = 8
Therefore, planet Y's orbital period is larger by (8/2.828) = 2.83 times.
When in doubt, draw a picture. The vertex of the equation is at (3,0) and the y-intercept is at (0,4.5). The answer is D