1. **State the problem:** We need to find the weight of each red block and each green block given two conditions: - 3 red blocks and 4 green blocks weigh 20 lbs. - 2 red blocks and 6 green blocks weigh 25 lbs. 2. **Set variables:** Let $r$ be the weight of one red block and $g$ be the weight of one green block. 3. **Write the system of equations:** $$3r + 4g = 20$$ $$2r + 6g = 25$$ 4. **Solve the system:** Multiply the first equation by 2 and the second by 3 to align coefficients of $r$: $$2(3r + 4g) = 2(20) \Rightarrow 6r + 8g = 40$$ $$3(2r + 6g) = 3(25) \Rightarrow 6r + 18g = 75$$ 5. **Subtract the first new equation from the second:** $$\cancel{6r} + 18g - (\cancel{6r} + 8g) = 75 - 40$$ $$18g - 8g = 35$$ $$10g = 35$$ 6. **Solve for $g$:** $$g = \frac{35}{10} = 3.5$$ 7. **Substitute $g=3.5$ into the first original equation:** $$3r + 4(3.5) = 20$$ $$3r + 14 = 20$$ 8. **Solve for $r$:** $$3r = 20 - 14 = 6$$ $$r = \frac{6}{3} = 2$$ **Final answer:** - Each red block weighs $2$ lbs. - Each green block weighs $3.5$ lbs.