Question

A man invests $5,200, part at 4% and the balance at 3%. If his total income for the two investments is $194, how much money did he invest at each rate?

Answer 1

Do you need a system of equations?
If so this will work.

Let's call x the amount he invested at 4% and y the amount he invested at 3%.
The total investment is $5200, so that gives us the first equation:
x + y = 5200

Now we deal with the interest.
4% of x is 0.04x, and 3% of y is 0.03y.
The total amount of interest he earned is $194, so that gives us the second equation:
0.04x + 0.03y = 194

Now you have a system of two equations in two unknowns, so you can solve for x and y.