#### Answer

x = 100

#### Work Step by Step

1. Given: 0.09x + 0.13(x + 300) = 61
2. Distribute: 0.09x + 0.13x + 39 = 61
3. Multiply both sides by 10 to the 2nd power to turn decimals into whole numbers:
100(0.09x + 0.13x + 39) = (61)100
9x + 13x + 3900 = 6100
4. Add and subtract: 22x = 2200
5. Divide: x = 100
6. Check: 0.09*100 + 0.13(100 + 300) = 61
The equation is true, so 100 is a correct solution of the equation.