Question

1. Investment. Part of $25,000 is invested at 10 percent, another part is invested at 12 percent, and a third part is invested at 16 percent. The total yearly income from these three investments is $3,200. Furthermore, the income from the 16 percent investment yields the same amount as the sum of the incomes from the other two investments. How much is invested at each rate?

Answer 1

Suppose x is invested at 10%, y is invested at 12% and z is invested at 16%. Here is what you know:
x + y + z = 25,000
0.10 x + 0.12 y + 0.16 z = 3200
0.16 z = 0.10 x + 0.12 y

You can immediatley write
2*(0.16 z) = 0.32z = 3200
So z = $10,000

Therefere x + y = $15,000.
You also know that
0.10x + 0.12 y = 1600

Now finish it. You have two equations in two unknowns left.