Final answer:
To determine the values of x and y for a stack containing 99 blocks that are 3 blocks tall, we divide the total number of blocks (99) by the height (3) to find the area of the base (33). Then, we look for factor pairs of 33 to get possible dimensions for x and y, which are (1, 33), (33, 1), (3, 11), or (11, 3).
Step-by-step explanation:
Given a stack containing 99 blocks that are 3 blocks tall, to find the possible values of x blocks long and y blocks wide, we need to use the concept of volume in mathematics. The volume of a rectangular prism (or stack of blocks in this case) is calculated by multiplying the length, width, and height. Now, our stack's height is given as 3 blocks, and hence, the volume of the stack, which is the total number of blocks (99), can be written as:
99 = x * y * 3
To find possible values of x and y, we divide the total volume (99 blocks) by the height (3). This gives us the area of the base of the stack:
33 = x * y
Now, we need to find two integers x and y, such that their product is 33. The factors of 33 that are integers are 1, 3, 11, and 33. Hence, possible pairs (x, y) could be (1, 33), (33, 1), (3, 11), or (11, 3). Any of these pairs are valid dimensions for length and width that will yield a stack with 99 blocks in total when multiplied by the height, which is 3 blocks.