An actor invested some money at 7% simple interest, and $37,000 more than four times the amount at 10%. the total annual interest earned from the investment was $49,290. how much did he invest at each amount?

Let the amt invested at 7% be represented by x.
Then the amt invested at 10% would be 4x + 37000.

The amts of interest that add up to $49290:
 
0.07x      + 0.10[4x+37000] = 49290

Then 0.07x + .40x + 3700 = 49290

Combining like terms, 0.47x = 45590.  Then x = $97000.

$97000 was invested at 7% and 4($97000) + $37000, or $425000, at 10%.