Question

The sum of two consecutive integers is at least 185. What is the smaller of the two integers?

Answer 1

Answer:  The smaller of two integers is at least 92.

Step-by-step explanation:  Given that the sum of two consecutive integers is at least 185.

We are to find the smaller of the two integers.

Let the two consecutive integers be n and n+1.

According to the given information, we have

$n+(n+1)\geq185\\\\\Rightarrow 2n+1\geq 185\\\\\Rightarrow 2n\geq185-1\\\\\Rightarrow 2n\geq184\\\\\Rightarrow n\geq\dfrac{184}{2}\\\\\Rightarrow n\geq92.$

Thus, the smaller of two integers is at least 92.

Answer 2

N + (n+1) = 185
2n + 1 = 185
2n = 184
n = 92
n is smaller than (n+1), so 92 is smaller, and 93 is the second number.