Let x be the starting amount for the account with 1% and y be the starting amount for the account with 2.5%. The amount after 3 years in account with 1%: x*1.01*1.01*1.01 = 1.030301x and amount after 3 years in the other account: y*1.025*1.025*1.025=1.0768906y. We know that x+y=1000 so y=x-1000. And we also know 1.0768906y + 1.030301x = 1055. Now we can replace the y in that equation with y=1000-x: 1.0768906(1000-x)+ 1.030301x = 1055 which can be simplified to x=469.86 and y is then y=1000-469.86=530.14 we can verify the answer: 469.86*1.030301 + 530.14*1.0768906= 1055 so 469.86 is correct.
