Final answer:
The problem is a mathematical exercise involving the sharing of fractions of a cake. It requires finding combinations of fractions from two people, X and Y, that when added together amount to 3/4 of a cake for the third person, Z. Possible combinations could include (1/2, 1/4), (1/4, 1/2), (3/8, 3/8), among others.
Step-by-step explanation:
The question explores the sharing of cake proportions between three individuals, X, Y, and Z, and inquires about the possible parts of the cake that X and Y could have given to Z, assuming Z ended up with 3/4 of a cake in total. We understand that this is a mathematical problem involving fractions, and we need to determine the possible fractions of the cake that could have been shared.
One approach to solve this problem is to look at the fractions of a pie as an analogy for the fractions of a cake. For instance, if we have one whole pie and we want to end up with 3/4 of it, we could slice the pie into four equal parts and take three (3/4). However, when we have contributions from two different pies (cakes in our scenario), the combinations can vary. X and Y could have split their cakes in different ways to give fractions that add up to 3/4 when combined.
Some possible combinations for X and Y to provide Z with 3/4 of a cake could include X giving 1/2 and Y giving 1/4, or X providing 1/4 and Y providing 1/2. Another scenario could be X giving 3/8 and Y giving 3/8, which also totals to 3/4. It's important to note that the sum of fractions from X and Y should equal 3/4, hence we can use the concept of common denominators or simply trial and error with simple fractions to find all the possibilities.