Given that x and y are positive whole numbers such that 2x+5y is divisible by 16, what are the possible values for x and y?

Step 1: Understand the conditions.
We are given that $x$ and $y$ are positive whole numbers, which means $x \ge 1$ and $y \ge 1$.
We are also given that $2x+5y$ is divisible by 16. This can be written as:

$$2x+5y = 16k$$

where $k$ is a positive integer.
Since $x \ge 1$ and $y \ge 1$, the smallest possible value for $2x+5y$ is $2(1)+5(1) = 7$.
Therefore, $16k \ge 7$, which implies $k \ge \frac{7}{16}$. Since $k$