Question

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?

n2 + n – 210 = 0
n2 + n – 105 = 0
2n2 + 2n + 210 = 0
2n2 + 2n + 105 = 0

Answer 1

Let the numbers be n and n+1. Half their product is (1/2)n(n+1)=105. Multiply both sides by 2:

n(n+1)=210 → n^2 + n − 210 = 0.

So the correct equation is n^2 + n − 210 = 0.