Expert: Bobby Soltani - 10/14/2005

Question
Hello:

I'm not certain how to solve the following:

0.08x + 0.075y = $464
x + y = $6000

Can you demonstrate, not tell, how to determine the solution for the above equation in more detail?

Here is a situation for using this equation:
An amount is invested at 8% and another amount is invested at 7.5%. 8% of some unknown amount plus 7.5% of some unknown amount is equal to $464. The first unknown  plus the other unknown is equal to $6000 since that is the total amount invested.

I thank you for your reply.

Answer
Hi,

0.08x + 0.075y = $464
x + y = $6000

Solve the second equation for x by subtracting y from both sides.

x = 6000 - y

plug this in for x in the first equation.

0.08(6000 - y) + 0.075y = 464

Now we have an equation with only one variable so we can solve it.

480 - 0.08y + 0.075y = 464
subtract 480 from both sides
-0.08y + 0.075y = -16
-0.005y = -16
divide both sides by -.005
y = 3200

Plug this into x = 6000 - y to solve for x.

x = 6000 - 3200 = 2800

Let me know if you have any questions.

Bobby