For this problem, we need to use the basic interest formula, I=Prt (Interest equals principal multiplied by rate multiplied by time). We are told that the investment is for 1 year (t) and that the interest is $3,290 (I). The concern is that there are two rates and we do not know how much of our principal is applied to each rate. We must set our variables:
For our first rate of 5%, we will use a variable of x for our principal
For our second rate of 7%, our variable becomes 57,000-x (since the two variables must add to 57,000)
Now we can create our equation. We must note each investment separately in the equation;
3,290=x(.05)1 + (57,000-x).07(1)
35,000=x Remember that x is the investment at 5%.
So now we can solve for our second investment;
7% Investment: 57,000-x