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

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

Check

(-15) * (-14) / 2 =

210/2

105 It does check.

The numbers are n and n + 1

Average = Av = 105