1. **State the problem:** Given the equation $$R_G T_G + R_B T_B = 120$$ with $$R_G = 4$$, $$R_B = 10$$, and the relation $$T_G = T_B + 2$$, find the values of $$T_G$$ and $$T_B$$. 2. **Write the formula and substitute known values:** The equation is $$4T_G + 10T_B = 120$$. Using $$T_G = T_B + 2$$, substitute into the equation: $$4(T_B + 2) + 10T_B = 120$$. 3. **Simplify and solve for $$T_B$$:** $$4T_B + 8 + 10T_B = 120$$ Combine like terms: $$14T_B + 8 = 120$$ Subtract 8 from both sides: $$14T_B + \cancel{8} - \cancel{8} = 120 - 8$$ $$14T_B = 112$$ Divide both sides by 14: $$\frac{14T_B}{\cancel{14}} = \frac{112}{\cancel{14}}$$ $$T_B = 8$$. 4. **Find $$T_G$$ using the relation:** $$T_G = T_B + 2 = 8 + 2 = 10$$. **Final answer:** $$T_G = 10, \quad T_B = 8$$