SOLUTION: Larry Mitchell investged part of his $10,000 advance at 7% annual simple interest and the rest at 4% annual simple interest. If his total yearly interest from both acccounts was $6

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Question 199077: Larry Mitchell investged part of his $10,000 advance at 7% annual simple interest and the rest at 4% annual simple interest. If his total yearly interest from both acccounts was $640, find the amount invested at each rate.
The amount invested at 7% is $_____
The anount invested at 4% is $_____
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=Amount he invested at 7% and y=Amount he invested at 4%

Since he has a total of $10,000, this means that x%2By=10000

Also, since he invested some at 7% and the rest at 4%, and received $640, this tells us that 0.07x%2B0.04y=640


7x%2B4y=64000 Multiply both sides by 100 to make every number whole.



So we have the system of equations:


system%28x%2By=10000%2C7x%2B4y=64000%29


-7%28x%2By%29=-7%2810000%29 Multiply the both sides of the first equation by -7.


-7x-7y=-70000 Distribute and multiply.


So we have the new system of equations:
system%28-7x-7y=-70000%2C7x%2B4y=64000%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28-7x-7y%29%2B%287x%2B4y%29=%28-70000%29%2B%2864000%29


%28-7x%2B7x%29%2B%28-7y%2B4y%29=-70000%2B64000 Group like terms.


0x%2B-3y=-6000 Combine like terms.


-3y=-6000 Simplify.


y=%28-6000%29%2F%28-3%29 Divide both sides by -3 to isolate y.


y=2000 Reduce.


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-7x-7y=-70000 Now go back to the first equation.


-7x-7%282000%29=-70000 Plug in y=2000.


-7x-14000=-70000 Multiply.


-7x=-70000%2B14000 Add 14000 to both sides.


-7x=-56000 Combine like terms on the right side.


x=%28-56000%29%2F%28-7%29 Divide both sides by -7 to isolate x.


x=8000 Reduce.


So the solutions are x=8000 and y=2000.


This means that he invested $8,000 at 7% and $2,000 at 4%