the sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times 5 the larger
n and n+1
n + n + 1 </= 9n - 5(n+1)
2 n + 1 </= 4 n - 5
2 n >/= 6
n >/= 3
To solve this problem, let's first assign variables to the two consecutive integers. Let's call the smaller integer 'x' and the larger integer 'x+1', since the two integers are consecutive.
The sum of these two consecutive integers is x + (x+1).
The difference between nine times the smaller and five times the larger is (9x - 5(x+1)).
According to the problem, the sum of the two consecutive integers is at most the difference between nine times the smaller and five times the larger. In other words, we can write the inequality as:
x + (x+1) ≤ (9x - 5(x+1))
Now, let's solve this inequality step by step:
x + (x+1) ≤ (9x - 5x - 5)
Simplifying the left side of the inequality:
2x + 1 ≤ (4x - 5)
Moving all terms to the left side:
2x - 4x ≤ -5 - 1
Simplifying:
-2x ≤ -6
Dividing by -2 (notice that we divide by -2 and change the direction of the inequality):
x ≥ -6/-2
Simplifying:
x ≥ 3
So, the smaller integer, 'x', must be greater than or equal to 3. The larger integer, then, is 3+1=4.
Therefore, the two consecutive integers are 3 and 4.