On two investments totaling $10,500, Brian lost 6% on one and earned 8% on the other. If his net annual receipts were $497, how much was each investment?

Let

x = the amount invested on the winner, then

10500-x = amount invested on the losing investment.

We know that the net profit is $497, so

0.08x - 0.06 (10500-x) = 497

Solve for x:

0.14x = 497+630=1127

x=1127/0.14=8050

Therefore Brian invested $8050 on the investment that earned 8% and $2450 on the one that lost 6%.