SOLUTION: Bob invested $20,000, part at 14% and part at 13%. If the total interest at the end of the year is $2,720, how much did he invest at 14%?

Question 55136: Bob invested $20,000, part at 14% and part at 13%. If the total interest at the end of the year is $2,720, how much did he invest at 14%?
Answer by Hook(36) (Show Source): You can put this solution on YOUR website!
Lets call x the amount that Bob invested at 14% and y the amount that he invested at 13%.
Combined, Bob invested 20 grand, so we have

Additionally, we know that the sum of the amount that Bob invested at 14% and 13% is equal to $2720. In math-speak, that says:

So we have the following system of equations:

My strategy will be to use the substitution method.
Starting with
and solving for x, I get

I'll plop that into the second equation

Great! Bob invested $8000 at 13%
I'll put that back into to find x

So the answer is Bob invested $12000 at 14%
CHECK:
I'll check my work by plugging x = 12000 and y = 8000 into the second equation

...check!
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