Question

Half of the product of two consecutive numbers is 105. To solve for n, the smaller of the two numbers, which equation can be used?

A.) n^2 + n – 210 = 0
B.) n^2 + n – 105 = 0
C.) 2n^2 + 2n + 210 = 0
D.) 2n^2 + 2n + 105 = 0

Answer 1

A.) n^2 + n – 210 = 0

Explanation:

just took edg 2022. hope this helps!

Answer 2

A

Explanation:

Consecutive nnumbers are spaced 1 units apart.

Such as 4,5,6,...

or 12,13,14,...

Thus,

if smaller number is n, then the next number (consecutive) is n+1

Since, half of the product of them is 105, we can write the equation as:

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

We can do some algebra and make it in quadratic form as shown below:

`(1)/(2)((n)(n+1))=105\\(1)/(2)(n^2 + n)=105\\n^2+n=2*105\\n^2+n=210\\n^2+n-210=0`

Answer choice A is right.