The cost of purchasing two commodities is $827. If the purchase price of the first one exceeds the other by $127, what is the purchase price of the first commodity? Give me reasons, before answering the question
Let X be the price of the first commodity, so the price of the second commodity is X - $127. The cost of purchasing two of them is X + (X - $127) = $827. Combining like terms, we get X * 2 - $127 = $827. Subtracting $137 from both sides, we get X * 2 = $954. Dividing both sides by 2, we get X = $477. So the final answer is 477.