SOLUTION: I am stumped on these kinds of word problems. You guys helped me a lot with the coin type and now I am stuck on the interest. If anyone can give me a step by step on how to set i

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Question 624037: I am stumped on these kinds of word problems. You guys helped me a lot with the coin type and now I am stuck on the interest. If anyone can give me a step by step on how to set it up to solve that would be great. You don't have to solve it for me just show me how to set it up. Thanks so much.
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?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
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?
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:

            %28matrix%286%2C1%2C%0D%0A%0D%0AAmount%2C+of%2C+interest%2C+at%2C+lower%2C+rate%29%29 + %28matrix%286%2C1%2C%0D%0AAmount%2C+of%2C+interest%2C+at%2C+higher%2C+rate%29%29 = %28matrix%284%2C1%2CTotal%2Camount%2C+of%2Cinterest%29%29

             .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