I am going to assume that the problem is supposed to say something along the lines of:
"A bank loaned out $15,000, part of it at the rate of 9% per year and the rest at 17% per year. If the interest received in one year totaled $2000, how much was loaned at 9%?"
Let's go over how to set it up:
Let X = amount invested at 9%
Y = amount invested at 15%
Since $15,000 was invested out, our first equation is:
X+Y=15000
Now, since the $15000 was invested partly at 9% and partly at 15% and the total interest is $2000, our second equation is:
0.09x+0.15Y=2000
So, our two equations are:
X+Y=15000
0.09X+0.15Y=2000
Multply everything in the first equation by -15 and everything in the second equation by 100 to get:
-15X - 15Y = -225000
9X + 15Y = 200000
If we add like-terms together, we get the equation:
-6X = -25000
Dividing both sides by 6 gives us:
X =$4166.67
So, the amount invested at 9% interest is $4166.67
