Answer :
$360
Let's assign the variable x for the amount invested at 5%. That means that (1200-x) will be the amount invested at 7.5%. So the equation becomes:
0.05x + 0.075(1200-x) = 81
0.05x + 90 - 0.075x = 81
-0.025x + 90 = 81
90 = 81 + 0.025x
9 = 0.025x
360 = x
So $360 was invested at 5% and the remaining ($1200 - $360 = $840 was invested at 7.5%.