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?

Answer 1

Givens

The numbers are n and n + 1

Average = Av = 105

Equation

Av = (n)(n + 1)/2

Solution

Av = 105

n(n +1)/2 = 105    Multiply both sides by 2

n(n + 1) = 105 * 2

n(n + 1) = 210      Remove the brackets.

n^2 + n = 210     Subtract 210 from both sides

n^2 + n - 210 = 0

factor

(n+15)(n - 14)

n + 15 = 0

n = - 15

n = - 15 which is the smallest of the two answers.

n + 1 = - 14