Half of the product of two consecutive numbers is 105. Which equation can be used to solve for n, the smaller of the two numbers?

If the smaller number is n, the consecutive number after it is n + 1. Their product is n(n + 1), and half of that product is 105, so n(n + 1)/2 = 105. Multiplying both sides by 2 and rearranging gives n² + n − 210 = 0, which is choice A.

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