Solve using a linear equation where x is the amount invested in the higher yeilding account. Solve for x

.06 (2x) + .10x = 9416

.12x +.10x = 9416

.22x = 9416

x = 42800

So he invests $42800 in the higher yeilding account, while investing 2x = $85600 in the other account.

Check.