One thing I would REALLY like to encourage you to do is to allow the notation to help you. Clean notation probably is more organized than your brain.
It took me a while to figure out what you were doing. You have a cute trick for solving some of these problems, but it seems it still lacks consistency and organization.
You write 75/100 = 37.46/x
That is lovely, but you have not defined 'x'. What is it? If you WRITE DOWN what it means, you will become confused far less often.
Let's try this one:
"A merchant marks up the wholesale price of an item by 25% to obtain its retail price. Later on she puts the item on sale for 25% off. If the sale price was $37.46, what was its wholesale price? "
W = The Wholesale Price
Markup = W * 0.25
Retail Price = W + W*0.25 = W*(1.25)
Discount = W*(1.25)*0.25
Discounted Price = W*(1.25) - W*(1.25)*0.25 = W*(1.25)*(1-0.25) = W*(1.25)*0.75 = 37.46
Thus, W = (37.46/0.75)/1.25 = 39.96
I see that you did manage the correct answer, but it requires substantial thought to see why. This may be why it took you longer than you expected to get it. The simpler you keep it, and the better you document it, the more consistent and understandable the result and the process.
