In one year, michael earned $6300 as a work study in college. he invested part of the money at 9% and the rest at 7%. if he received a total of $493 in interest at the end of the year, how much was invested at 7%? how much was invested 9%?

Let x represent invested money at 9% and y at 7%
Now we write system:
x+y = 6300
1.09*x + 1.07* y = 6300 + 493 = 6793

1.09x + 1.09y = 6867
Here we multiplied first equation with 1.09 and now we will subtract second from first:

0.02y = 74
y = 3700
x = 6300-3700 = 2600

Michael invested 2600 at 9% and 3700 at 7%

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