Question

The sum of two consecutive integers is at most 223. What is the largest possible integer? Enter your answer in the box.

a) 110
b) 111
c) 112
d) 113

Answer 1

The largest possible integer among two consecutive integers that sum to at most 223 is 112. After solving the inequality, we determine that the correct answer is option c) 112.

Step-by-step explanation:

To solve the mathematical problem presented, we will use the concept of consecutive integers. Two consecutive integers can be represented as n and n + 1. The question states that their sum is at most 223, which is given by the inequality n + (n + 1) ≤ 223. Solving this inequality, we combine like terms to get 2n + 1 ≤ 223. Subtracting 1 from both sides, we get 2n ≤ 222. Dividing both sides by 2, we find n ≤ 111. Given n is the smaller of the two integers, n + 1 will give us the larger integer.

Therefore, we find that the largest possible consecutive integer, in this case, is 111 + 1 which equals 112. Hence, the largest possible integer is 112.

We conclude that the correct option answer in the final answer is c) 112.