HELP! percent problem?

I cant figure this one out.. i dont know the equation or how to solve the equation.. here is the problem

u have 500,000 in an ira when you retire. i have the option to invest the money into 2 funds, fund A pays 5.2% Fund B 7.7% both annually. how should you divide your money between fund A and fund B to produce annual interest income of 34,000

if someone could give me the equation and explain how the steps in answering it i would really appreicate it.. thanks

two simultaneous equations (8th grade algebra)

you want X*5.2% + Y*7.7% = 34000/500000
and you want X+Y=100%

.052X + .077Y = .068
X + Y = 1
multiply second equation by -.052 to get rid of X part

.052X + .077Y = .068
-.052X - .052Y = -.052
now add the two equations vertically
0X +.025Y = .016 therefore Y = .64
and by sunstitution into X+Y=1 you get X =.36

so you want .36*500000 in fund A and .64*500000 in fund B

The answer is $100,000 in fund A and $400,000 in fund B. I solved the problem using algebra. Using the facts, we come up with the following equations:

A=the amount of money that should be invested in fund A
B=the amount of money that should be invested in fund B

A+B=$500,000 (the total available when you retire)

5.2%(A) + 7.2%(B)=$34,000

Since A+B=$500,000, we know that B=$500,000-A

When we subsitute B with the above equation, we get

5.2%(A) + 7.2%(500,000-A)=$34,000
5.2%(A) + $36,000 - 7.2%A=$34,000
-2%A + $36,000=$34,000
-2%A =-$2,000
A=$100,000

Since A+B =$500,000, we know B=$400,000

you would want to invest 320,000 at 7.7% and 180,000 at 5.2% to get a yield of exactly 34,000. I know there's probably a formula, but I just simulated the question on a spreadsheet and quit when the answer came out right.