Given the details presented, we know that Ethan earns $30 a day with an additional $4 for each sale he makes. Similarly, Oscar earns $24 a day plus $6 for each sale.
We formulate these relationships into equations, assigning 'n' as the number of sales. For Ethan, his earning equation is "4n + 30" and for Oscar, his earning equation is "6n + 24".
Now, we want to find when their earnings are equal or in other words, when both equations are equal to each other. This will give us the equation:
4n + 30 = 6n + 24
This equation is describing the relationship between Ethan's and Oscar's earnings when they have the same number of sales.
If we look at the given options a, b, c, and d, our derived equation matches with option: 'a. 4n + 30 = 6n + 24'.
Therefore, the answer is 'a. 4n + 30 = 6n + 24'.