Expert: Paul Klarreich - 12/5/2008

Question
I need to find out the answer to this question,
using Elimenation or Substitution.

Ian invested $8000, part at 9% per annum and the remainder at 10% per annum. After one year his total interest $740.00. How much did he invest at each rate?

Answer
Questioner:   britt
Category:  Advanced Math
Private:  No
 
Subject:  Elimenation and Substitution
Question:  I need to find out the answer to this question,
using Elimenation or Substitution.

Ian invested $8000, part at 9% per annum and the remainder at 10% per annum. After one year his total interest $740.00. How much did he invest at each rate?
.................................
Hi, Britt,

This belongs to a whole category of problems called Rate-time-distance.  The words may change, but not the problem.

The basic rule is:

Something * something else = a value.

In this case, it's:

Int rate * principal = interest paid.


Set up these boxes to make your variable(s) clear.  I assume you will be doing this using TWO variables.
Which investment    Rate        Principal     Paid
------------------+------------+------------+-------------+
At 9%                 0.09          x          0.09x
------------------+------------+------------+-------------+
At 10%                0.10          y          0.10y
------------------+------------+------------+-------------+
Total                             8000         740
------------------+------------+------------+-------------+

OK, now there are some logical totallings:

   x +     y = 8000
0.09x + 0.10y = 740

Now clear fractions (you know how to do that) and solve.