The Three Investments

14)  Jill made three investments that yielded $2,260 as annual
interest.  Her 7.5% investment was $7,000 more than the one at
5%, and her 8% investment was $1,000 less than six times the 5%
investment.   What was the amount she paid for each of these investments?

"x" will be the variable for the 5% investment.  We, therefore,
will figure the other investments on the bases of that.

        .05(x) + .075(x + 7,000) + .08(6x - 1,000) = 2260.00

Now move the decimal point two places to the right:

        5(x) + 7.5(x + 7,000) + 8(6x - 1,000) = 226,000

Then add:

        5x + 7.5x + 52,500 + 48x -8,000 = 226,000

Combine like signs:

        60.5x + 44,500 = 226,000

Isolate x to one side of the equal sign by performing the operation
of deleting 44,500 from both sides:

        60.5x = 181,500

Divide both sides by 60.5 to find the value of x:

        x = 3,000

We can now plug the value of x into the formula:

        5(x) + 7.5(x + 7,000) + 8(6x - 1,000) = 226,000

                5%   =  $3,000
                7.5% = $10,000 (x + 7,000)
                8% =   $17,000 (6x - 1,000)

To find the annual interest yield of each one, convert the percents
back to decimals by dividing them by 100.  Then multiply:

                                                             
               Investment                   Interest Earning

          5% divided by 100 = .05       .05 *  $3,000 =   $150.00    
        7.5% divided by 100 = .075     .075 * $10,000 =   $750.00
          8% divided by 100 = .08       .08 * $17,000 = $1,360.00
                                              --------------------               
                                              $30,000   $2,260.00
  
We can also divide 2,260 by 30,000 to find out what are average
percent rate was for all three investments: 7.53%