SOLUTION: 3. One year ago Walt invested $12,000. He invested part of the money at 7% and the rest at 9%. He made a total of $970 in interest. How much was invested at 7%? I tried to figure

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Question 199080: 3. One year ago Walt invested $12,000. He invested part of the money at 7% and the rest at 9%. He made a total of $970 in interest. How much was invested at 7%?
I tried to figure this out and I need a hand with this problem
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 9%

Since he has a total of $12,000, this means that x%2By=12000

Also, since he invested some at 7% and the rest at 9%, and received $970, this tells us that 0.07x%2B0.09y=970


7x%2B9y=97000 Multiply both sides by 100 to make every number whole.



So we have the system of equations:


system%28x%2By=12000%2C7x%2B9y=97000%29


-7%28x%2By%29=-7%2812000%29 Multiply the both sides of the first equation by -7.


-7x-7y=-84000 Distribute and multiply.


So we have the new system of equations:
system%28-7x-7y=-84000%2C7x%2B9y=97000%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%2B9y%29=%28-84000%29%2B%2897000%29


%28-7x%2B7x%29%2B%28-7y%2B9y%29=-84000%2B97000 Group like terms.


0x%2B2y=13000 Combine like terms.


2y=13000 Simplify.


y=%2813000%29%2F%282%29 Divide both sides by 2 to isolate y.


y=6500 Reduce.


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-7x-7y=-84000 Now go back to the first equation.


-7x-7%286500%29=-84000 Plug in y=6500.


-7x-45500=-84000 Multiply.


-7x=-84000%2B45500 Add 45500 to both sides.


-7x=-38500 Combine like terms on the right side.


x=%28-38500%29%2F%28-7%29 Divide both sides by -7 to isolate x.


x=5500 Reduce.


So our answers are x=5500 and y=6500.


This means that he invested $5,500 at 7% and $6,500 at 9%