1. **State the problem:** We have three types of bags: wheat (W), corn (C), and oats (O). The problem gives us relationships between their weights and asks for the weight of one bag of wheat. 2. **Write the given equations:** - Three bags of wheat, two bags of corn, and one bag of oats weigh the same as one bag of wheat, one bag of corn, and five bags of oats: $$3W + 2C + O = W + C + 5O$$ - Two bags of corn and one bag of oats weigh 26 pounds: $$2C + O = 26$$ - One bag of corn weighs 10 pounds: $$C = 10$$ 3. **Simplify the first equation:** $$3W + 2C + O = W + C + 5O$$ Subtract $W + C + 5O$ from both sides: $$3W + 2C + O - W - C - 5O = 0$$ Simplify: $$2W + C - 4O = 0$$ So, $$2W + C = 4O$$ 4. **Use the known value of $C$ to find $O$:** From the second equation: $$2C + O = 26$$ Substitute $C = 10$: $$2(10) + O = 26$$ $$20 + O = 26$$ $$O = 26 - 20 = 6$$ 5. **Find $W$ using the simplified first equation:** $$2W + C = 4O$$ Substitute $C = 10$ and $O = 6$: $$2W + 10 = 4(6)$$ $$2W + 10 = 24$$ Subtract 10 from both sides: $$2W = 14$$ Divide both sides by 2: $$W = 7$$ **Final answer:** One bag of wheat weighs **7 pounds**.