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

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) (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

Also, since he invested some at 7% and the rest at 4%, and received $640, this tells us that

Multiply both sides by 100 to make every number whole.

So we have the system of equations:

Multiply the both sides of the first equation by -7.

Distribute and multiply.

So we have the new system of equations:

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

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

------------------------------------------------------------------

Now go back to the first equation.

Plug in .

Multiply.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the solutions are and .

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

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