SOLUTION: Melody Has $45,000 to invest and wishes to receive an annual income of $4290 from this money. She has chosen investments that pay 5%, 8%, and 12% simple interest. Melody wants to h

Question 43727: Melody Has $45,000 to invest and wishes to receive an annual income of $4290 from this money. She has chosen investments that pay 5%, 8%, and 12% simple interest. Melody wants to have the amount invested at 12% to be double the amounted invested at 8%. How much should she invest at each rate.
Answer by mbarugel(146) (Show Source): You can put this solution on YOUR website!
Hello!
This can be solved with a system of 3 equations and 3 unknowns. Let's call X to the amount invested at 5%, Y to the amount invested at 8% and Z to the amount invested at 12%.
Since she has $45,000, we have:

We also know that "Melody wants to have the amount invested at 12% to be double the amounted invested at 8%". Therefore,

Finally, she "wishes to receive an annual income of $4290 from this money". Therefore, we get:

So we have the system:

This system can be solved with any method you prefer (for example, by substitution). The solutions are:
X=9000
Y=12000
Z=24000
Therefore, she should invest $9,000 at 5%, $12,000 at 8% and $24,000 at 12%

I hope this helps!
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