Question 1122414

Paul has $40,000 to invest.  his intent is to earn 6% interest on his investment.  He can invest part of his money at 5% and part at 9% interest.  How much does Paul need to invest in each option to make a total of 6% return on his $40,000?  I don't even know where to start with this.  I have no clue how to put this into equation form.  I would appreciate a little help.  THANK YOU!!!
<pre>Let amount that he needs to invest at 5% be F
Then amount he needs to invest at 9% is: 40,000 - F
We then get the following EARNINGS equation: .05F + .09(40,000 - F) = .06(40,000)
.05F + 3,600 - .09F = 2,400
.05F - .09F = 2,400 - 3,600
- .04F = - 1,200
F, or amount he needs to invest at 5% = {{{highlight_green(matrix(1,3, (- "1,200")/(- .04), "=", "$30,000"))}}}
Amount he needs to invest at 9% = {{{highlight_green(matrix(1,3, "$40,000" - "$30,000", "=", "$10,000"))}}}
You need to do your own check!