Subjects algebra

Rope Length 72A049

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1. **State the problem:** We have 3 pieces of rope with lengths in the ratio 2:3:5, and their combined length is 80 feet. 2. **Set up variables:** Let the lengths be $2x$, $3x$, and $5x$. 3. **Write the equation for total length:** $$2x + 3x + 5x = 80$$ 4. **Simplify the equation:** $$10x = 80$$ 5. **Solve for $x$:** $$x = \frac{80}{10} = 8$$ 6. **Find the length of the longest piece:** $$5x = 5 \times 8 = 40$$ 7. **Cut the longest piece in half:** Each half is $$\frac{40}{2} = 20$$ **Final answer:** Each half of the longest piece is 20 feet long. **Answer choice:** C. 20