Question 624037
You have a total of $10,000 to invest in two simple interest accounts. On one account the annual simple interest rate is 3.5%. On the second account the annual simple interest rate is 7.5%. If you earn $520 per year from these two investments, how much do you have invested in each account?
<pre>
Make this chart:

                | Amount invested  | Rate  | Amount of interest |                      
at lower rate   |                  |       |                    |
at higher rate  |                  |       |                    |
-----------------------------------------------------------------
Total           |                  |||||||||                    |

Let's let $x be the amount invested at the lower rate.
Then $10000-$x will be the amount invested at the higher rate,
and the total amount invested will be $10000.  We fill those in:

                | Amount invested | Rate  | Amount of interest | 
at lower rate   |       x         |       |                    |
at higher rate  |    10000-x      |       |                    |
-----------------------------------------------------------------
Total           |     10000       |||||||||                    |

Fill in the rates as decimals:
Fill in the amount of interest by multiplying the rate by the amount invested
Fill in the total amount of interest received as $520

                | Amount invested | Rate  | Amount of interest | 
at lower rate   |       x         | .035  |       .035x        |
at higher rate  |   10000-x       | .075  |  .075(10000-x)     |
-----------------------------------------------------------------
Total           |    10000        |||||||||        520         |


The equation comes from:

            {{{(matrix(6,1,

Amount, of, interest, at, lower, rate))}}} + {{{(matrix(6,1,
Amount, of, interest, at, higher, rate))}}} = {{{(matrix(4,1,Total,amount, of,interest))}}}

             .035x + .075(1000-x) = 520

Solve that and get x = $5750

Therefore the answer is:  

x = $5750 at the lower rate of 3.5%

10000 - x = 10000 - 4250 = $4250 at 7.5%

Edwin</pre>