Pumpkin Watermelon 29D047

1. **State the problem:** We have two scales with pumpkins and watermelons. The first scale shows 3 pumpkins and 2 watermelons weighing 27.5 pounds. The second scale shows 4 pumpkins and 3 watermelons weighing 37.5 pounds. We want to find the weight of one pumpkin and one watermelon. 2. **Define variables:** Let $p$ be the weight of one pumpkin and $w$ be the weight of one watermelon. 3. **Write the system of equations:** $$3p + 2w = 27.5$$ $$4p + 3w = 37.5$$ 4. **Solve the system using elimination:** Multiply the first equation by 3 and the second by 2 to align the coefficients of $w$: $$3(3p + 2w) = 3(27.5) \Rightarrow 9p + 6w = 82.5$$ $$2(4p + 3w) = 2(37.5) \Rightarrow 8p + 6w = 75$$ 5. **Subtract the second equation from the first:** $$ (9p + 6w) - (8p + 6w) = 82.5 - 75$$ $$ 9p - 8p + \cancel{6w} - \cancel{6w} = 7.5$$ $$ p = 7.5$$ 6. **Substitute $p = 7.5$ into the first original equation:** $$3(7.5) + 2w = 27.5$$ $$22.5 + 2w = 27.5$$ 7. **Isolate $w$:** $$2w = 27.5 - 22.5$$ $$2w = 5$$ $$w = \frac{5}{2} = 2.5$$ 8. **Final answer:** - One pumpkin weighs $7.5$ pounds. - One watermelon weighs $2.5$ pounds.