You start by assigning names to the things you want to find. You want to find how much she invested in in each bond so we will use "X" to represent the amount of money she invested in the first bond (at 4%) and "Y" to represent the amount of money she invested in the second bond (at 6%).

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 thehigher6% 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%mustgive between $48 and $72 interest.