James invested some money at 7% interest. james also invested $75 more than 2 times that amount at 13%. how much is invested at each rate if james receives $1105.35 in interest after one year? (round to two decimal places if necessary.)

Given: Let x be the investment

x at 7% interest - - > (1+0.07) x = 1.07x

$ (75+2x) at 13% interest = 1.13 (75+2x)

= 84.75 + 2.26x

If James receives $1105.35 by the end of the year, then:

1.07x + 84.75 + 2.26x = 1105.35

1.07x + 2.26x = 1105.35 - 84.75

3.33x = 1020.60

3.33x/3.33 = 1020.60/3.33

x = 306.4864 or 306.49

Next is substitute the value of x.

For 7% interest: 1.07 (306.49) = $327.94

For 13% interest: 84.75 + 2.26 (306.49) = $777.42