system of equations: 'investment' word problem

[KingAce]

heres the problem:

"A total of $15,000 is invested in two corporate bonds that pay 7.5% and 6% simple interest. The investor wants an annual interest income of $990 from the investments. What is the most that can be invested from the 6% bond?

What two systems of equations do I set up? Thank you!

 

[masters]

Try letting x represent one corporate bond amount invested and y represent the other. Together, they total 15,000. That's one equation. Then use the simple interest rule to find the second equation. That total will be 990. Then all you have to do is solve the system.

 

[soroban]

Hello, KingAce!

A total of $15,000 is invested in two corporate bonds that pay 7.5% and 6% simple interest.
The investor wants an annual interest income of $990 from the investments.
What is the most that can be invested from the 6% bond?

Organize the facts . . .


\(\displaystyle \begin{array}{ccc}\text{Let }x\text{ = amount invested at 6 percent} & \quad & \text{earns }0.06x\text{ dollars in interest} \\ \text{Let }y\text{ = amount invested at 7.5 percent} & \quad & \text{earns }0.075y\text{ dollars in interest} \\ \$15,000\text{ = total invested} & \quad &\$990\text{ = total interest} \\ \\ \downarrow & & \downarrow \\ \\ x + y \;=\;15000 & & 0.06x + 0.075y \;=\;990 \end{array}\)