You haven't translated it correctly. If the 'part' is x then the 'remainder' is 7500-x. So the total interest is x*0.05 + (7500-x)*0.04 which is equal to 346.5. That is, x*0.05 + 7500*0.04 - x*0.04 = 346.5. Collecting terms, x*(0.05-0.04) + 300 = 346.5 and simplifying x*0.01 = 46.5. Now divide by 0.01 (multiply through by 100) to get x.