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

Question

asked Dec 7, 2019 161k views

2 Answers

Ranguard · Answer 1 · 2019-12-14T04:53:40+0000

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.