What process do I use to solve the question below?

Question

A man has $100,000 to invest in 3 different funds. One fund yields a rate of 3% per year, a second yields 5% per year, and the third earns 9% per year. The annual earnings needed are $6,800. The amount at the 9% rate is twice as much as the amount invested at the 3% rate. Find the amount of money invested in each different fund.

Answer 1

Let the amounts invested in the 3%, 5% and 9% funds be x,y and z.

 

Now we can say from the first sentence:

 

x + y + z = 100000

 

Also we can write from the next two sentences:

 

.03x + .05y + .09z = 6800

 

Finally from the following sentence we can also see that:

 

z = 2x  

 

Substitue the 3rd equation into the 1st:

 

3x + y = 100000

 

Substitute this result into the 2nd equation and using the 3rd equation again:

 

.03x + .05(100000 - 3x)  + .09(2x) = 6800

 

Solve for x and get x = $30000

 

Using the 3rd equation we can see that z = 2(30000) = $60000

 

Therefore y = $10000