My question is Mr.Carter is very cautious. He decides to invest in only three stocks: one low stock, one high stock, one medium stock. Given that the expected annual yields are 6% for low stock, 7% for medium stock, and 8% for high stock, he wants his investment in medium stock to be half of his total investment in low and high stock. How much should I invest in each type fo stocks to expect a total annual return fo $650 form my investments? I was wondering if the set up is:

x+y+z=10,000
.06x+.07y+.08z=?

How do you get the rest?

I assume from the first line of your setup that the total investment is $10,000 and that the amounts invested in the low, medium and high yield stocks are $x, $y and $z respectively.

I agree with your first equation

You have three variables, x, y and z so you probably need another equation. Rerreading the problem I see "he wants his investment in medium stock to be half of his total investment in low and high stock". That is he wants y to be half of x + z. Thus the third equation is

I would now substitute this expression for y into the first two equations, simplify and then solve the resulting two equations for x and z. I'll substitute into the second equation for you and then you can do it with the first equation.

Since y = ^{(x + z)}/₂, the second equation