Two consecutive odd integers have a sum that is, at most, 36. What is the greatest value the larger number could have?
if x is the larger, x-2 is the smaller, since odd number differ by 2
So,
x-2 + x <= 36
solve for x
x + ( x+2) <= 36
X <= 17.
x+2 <= 19.
Therefore, x+2 = 19, max.
To find the greatest value the larger number could have, we need to consider the given conditions.
Let's assume the first odd integer is represented by x. Since the integers are consecutive, the next odd integer would be x + 2.
According to the problem, their sum should be at most 36. So, we can set up the following inequality:
x + (x + 2) ≤ 36
Now, let's solve this inequality to find the maximum value for the larger number:
2x + 2 ≤ 36
Subtracting 2 from both sides:
2x ≤ 34
Dividing both sides by 2:
x ≤ 17
From this, we can see that the maximum possible value for x is 17. Therefore, the larger number, x + 2, would be:
17 + 2 = 19
Hence, the greatest value the larger number could have is 19.