Now interpret each sentence as an equation. "Pat invested $1200" gives X+ Y= 1200. X dollars invested at 4% per annum yields .04X in one year and Y dollars invested at 6% per annum yields .06Y in one year. The total yield is .04X+ .06Y. "at the years end she had $1225" means she had her orginal $1200 and an additional $25: .04X+ .06Y= 25.
However, there is a difficulty with this problem! If she had invested all $1200 dollars at the lower 4%, she would have earned .04(1200)= $48. Investing some at the higher 6% can't give less than that and 25 is less than 48. I thought perhaps I had misunderstood and she earned the entire 1225 in interest but that is also not possible. If she had invested the full $1200 dollars at 6% she would have earned .06(1200)= 72 dollars and that's far smaller than 1225. Investing $1200 split between 4% and 6% must give between $48 and $72 interest.