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

n² + n - 210 = 0

Step-by-step explanation:

Answer 2

• First choice: n² + n - 210 = 0

Step-by-step explanation:

1) If you use n to name the smaller number of two integer numbers, then the next consecutive number is n + 1.

2) The product of those two numbers is n × (n + 1) = n (n + 1).

3) Half of that product is n (n + 1) / 2.

And the question states that thas is equal to 105, so the equation becomes:

4) n (n + 1) / 2 = 105

Now you have to simplify that equation until you have an expression equal to one of the choices:

5) Simplification:

• Multiply both sides by 2: n (n + 1) = 210

• Distributive property on the left side: n² + n = 210

• Subtract 210 from both sides: n² + n - 210 = 0

And that is the first choice, so you have your answer.