1. **State the problem:** Justin weighs 15 pounds less than Greg. Half of Greg's weight is 75 pounds less than Justin's weight. We need to find their weights. 2. **Define variables:** Let $G$ be Greg's weight and $J$ be Justin's weight. 3. **Write equations from the problem:** - Justin weighs 15 pounds less than Greg: $$J = G - 15$$ - Half of Greg's weight is 75 pounds less than Justin's weight: $$\frac{G}{2} = J - 75$$ 4. **Substitute $J$ from the first equation into the second:** $$\frac{G}{2} = (G - 15) - 75$$ 5. **Simplify the right side:** $$\frac{G}{2} = G - 90$$ 6. **Bring all terms to one side:** $$\frac{G}{2} - G = -90$$ 7. **Simplify the left side:** $$\frac{G}{2} - \frac{2G}{2} = -90$$ $$-\frac{G}{2} = -90$$ 8. **Multiply both sides by $-2$ to solve for $G$:** $$\cancel{-2} \times -\frac{G}{\cancel{2}} = -90 \times \cancel{-2}$$ $$G = 180$$ 9. **Find $J$ using $J = G - 15$:** $$J = 180 - 15 = 165$$ 10. **Check the options:** Greg weighs 180 pounds and Justin weighs 165 pounds, which matches option C. **Final answer:** Greg weighs 180 pounds, and Justin weighs 165 pounds.